I've written about this elsewhere, but let me repeat the argument while adding in some mathematical modelling which seems appropriate.
An important principle in my metatheory of science is that a more advanced theory should capture the valid insights of previous theories. Einstein didn't throw out Newton, he made him into a special case, valid under limited contexts. Humor Theory sought to explain while correcting previous theories and observations. Similarly a more advanced empirical psychology of religious experience should give some kind of explanation for common or long-held theological assertions, even if rejecting their antimaterialist ontologies. Etc.
Hence the question, Does, and if so how exactly does, Big5 make an advance on Myers Briggs? Can we capture MB's valid insights in a more advanced theory?
To summarize, these are two multidimensional personality theories, where the theory provides a small number of abstract dimensions and claims that each person's personality is to a great extent characterized by their individual values on these dimensions. That makes them close relatives in a certain family of theories.
But enthused by the narcissism of small differences, academics have declared one to be an advance on the other; while I will show them in detail to be the same, qua underlying theory, except one has one dimension the other lacks, and the other has another dimension the first lacks. I declare a tie!
In short, Big5 adds a useful Neuroticism dimension, while not-so-usefully removing the N/S or Universe dimension, but otherwise Big5 is underlyingly identical to Myers Briggs. This remarkable assertion can be justified under a mixture model analysis of both systems, showing that the differences are somewhere between trivial and terminological, except for Neuroticism and N/S.
May I take a short detour into mixture modelling?
Folks do mixture modelling in investment or portfolio theory. Suppose you have two specific investment ideas each of which is optimal in some sense, like, maximum expected return and minimum expected variability (e.g., S&P 500 and T-Bills). Put those down as points on a graph -- of return versus variability, say -- it is important that you can see them as different points in some kind of a space. Then by splitting your portfolio into a sum of both investments, some percentage, P, assigned to one, and the rest, 1-P, to the other, you can get any point on the line between your two pure investment ideas. That range of possible combined investments is called a mixture, and P and 1-P are called the weights of the mixture. A mixture is also nothing but a linear combination subject to the 100% rule: the two weights have to add up to 100%, and usually they also have to both be non-negative. Their idea is that by having a mixture model for your investments, you can achieve any outcome desired on this so-called optimal frontier of investment portfolios, based on the investor's personal preferences for maximizing return versus minimizing variability.
Stepping back, mixture modelling provides for a system in which there are actually and truly only two pure ideas or types representing categorically distinct values in some space, but then in the observed space you may see any kind of weighted combination of them.
Mixture weighting induces a continuum from discrete categories.
Ready to get back to Personality Theory? Let's consider if Extroversion/Introversion or any of the other binaries were actually mixture models. The Theory would provide two ideas of pure personality types to define a given dimension, and then the personality of an individual could end up actually being some mixture, a weighted (with weights summing to 100%) combination of the two. In a measurement space the population of individuals could be distributed continuously across the line segment or continuum between the two pure endpoints. Now is this a discrete model, or a continuous model? It is both, obviously. It is a mixture model.
We are ready to get back to the comparison of Myers Briggs and Big5. I hope I am not alone when I equate the single MB Perceiver/Judger dimension with the two dimensions of Openness and Conscientiousness: "Perceiver" being Open, and "Judger" being Conscientious. I think of Perceiver/Judger as a preference regarding for future versus past decision time, with Perceiver preferring to make decisions in the future (hence to put them off for now, and explore more), while Judger prefers that their decisions have been made in the past (hence to decide anything quickly that has not been decided yet, and explore less).
Clearly a person who remains Open regarding a decision has not made it yet (P), while a person who is Conscientious regarding any decision must consider it decided already (J). So these could be seen as equivalent pure types. Then the MB P/S dimension would be a mixture model between these two types which are logical opposites in terms of decision-time preference. In contrast the Big5 Openness and Conscientiousness dimensions would be two mixture models with Zero as the alternative pure type for both of them. Openness and Conscientiousness can each then range from 0 to 100%.
The mathematical or theoretical difference between MB and Big5 then would simply be whether, in the measurement space, the weights for the same two pure type endpoints are required to sum to 100% (MB) or in the case of Big5, they are allowed to sum to any value from 0% to 200%. If both are mixture models and both are based on the same pure types, and in this area of personality both have not four but only two pure types (plus zero, which hardly counts as anything, if I may put it that way), then the argument is not between MB and Big5 underlying pure Types, but between how those Types may be combined and measured.
Hence the parade we see of academic warriors running around with the decapitated heads of MB on their poles celebrating their victory, are really celebrating a rather tiny and technical difference in detail. Yes Mr. Brooks, I'm thinking about you.
Another correspondence between MB and Big5 is in the F/T vs Agreeability dimensions. T is traditionally for Thinker or Tough-mindedness; T's are in their heads, some say. Whereas F, traditionally Feelings-based, are in their hearts, so to speak. F's know they have feelings, and they know what their feelings are, and once they are socialized and adult they likely know the same about others, and therefore have a more cooperative style, and develop greater social and emotional intelligence. F means the same to me as Big5 "A for Agreeable". In a zero-based mixture model, the two analyses are exactly the same if we simply assert Zero Agreeability is the same as the ideal type of the T character. Hence the mixture model in both systems would have mixture parameters P and 1-P to weight the two end, and hence individuals being in each case some mixture of the two ideal endpoints would be shown on a graph as continuously distributed between the endpoints.
The difference between MB and Big5 in this case being reduced to whether the pure endpoint opposite to the Feelings based or Agreeable pure type is considered Zero Agreeable, or 100% Tough-minded. If that's a meaningful difference, I don't see it. Those are lexical relabellings of the same thing; each can be defined exactly in terms of the other; there is only one true idea there.
N for 'iNtuitive' and S for 'Sensory', goes the traditional MB terminology. S people live in the outer worlds of observables, facts, grounded reality. N people live in the inner worlds of intuition, ideas, systems, theory, deeper reality.
S people are 3/4 of the population (link), N are about 1/4.
The S/N difference has been important in my life because it has distinguished me from multiple romantic partners in failed relationships. As ENTP my match is INFJ, opposite in all dimensions except N/S, but I figured, like most of you, this MB stuff is baloney so who cares about N/S when you're in love.
In the end those relationships ended on a similar dynamic under stress. I'm very N, so let me give you my idea of the deeper reality which governs things here.
Since in general things break when they are under stress, we may assert that what matters for relationship durability is that you can handle stress together. But of course when an S person is under stress or in conflict they want to hear the facts, observables, times, places, names, actions, the grounded reality. Whereas when an N person is under stress or in conflict they want to hear the ideas, intuitions, generalizations, abstract reasons, the deeper reality. Both can be talking all the time while neither seems to the other to be saying anything. In stress they cannot reach each other, because they are operating in different Universes: the inner, and the outer. In order to last such relationships require somehow-reduced conflict and increased mutual surrender, or passivity, or low self-esteem or low sense of entitlement. If there are sparks and each believes in themselves, they will not be able to hold it together without finding some common ground, and in different universes there is no common ground. This is the importance of the N/S dimension.
May it also be said that a person who lacks a sense of theory and only knows facts will be unable to abstractly rearrange the furniture of life to come up with better ideas. They may be poor Field Marshals, Inventors, Architects, Masterminds, because their thinking is not flexible because it does not operate in the world of abstractions, and cannot find the higher and right level of abstraction to solve a problem which may admit of many concretely-different solutions. They may also be poor Counselors, Healers, Champions, Teachers, because they do not vibe with the inner intuitive understandings which allow such skills to emerge.
Therefore for me the N/S dimension is real and important, and the loss of it in Big5 is a Problem.
Without N/S, Big5 is not an advance in science but a step backwards. In particular it fails to capture an important and powerful difference which dooms a goodly portion of relationships, namely, those between N and S individuals.
How could this be the case? I'll tell you how. First, only 1/4 of people are N, most are not N, so they are harder to see, being fewer. Second, their qualities are invisible, and only come out in incomprehensible mutterings about unseen universes, which we reality-based people frankly don't need to acknowledge or think about, because We are in the Real world and That is all bullsh*t. The people who are not N cannot see the qualities of N people. They seem like regular concrete minded folks, but just aren't very smart or grounded in their sense of reality. They are less than, rather than different. This is how S people relate to N people. Believe me as a plumber I was not set up for success amongst a crowd of concrete minded thinkers; I was never so stupid as when I was an apprentice being evaluated by a concrete-minded foreman: quite stupid.
If N's are a small proportion of the population, and they are invisible to most of the subjects in your Big5 survey, then they won't much show up in your data. 3/4 will see nothing, and 1/4 will only see 1/4 of them. Therefore only 1/16 of your survey results will reflect their existence, and your data analysis and theory will ignore them. That's how.
If on the other hand you use only professionals, namely psychotherapists, who as it turns out are mostly intuitive Ns, therapists and counselors, and use them to do your Big5 personality survey, then you'll get people who are capable of detecting the N/S distinction. Better yet, your differences will not be instrumental or utility judgements of others, because instead of people looking at people (typically in terms of how they interact and can be useful for them) you have intuitives looking at people (typically in terms of how to understand their inner being).
Then N/S will show up in your data, if your PCA software can detect a difference that separates 1/4 to 3/4 of your population.
And the moral judgement implicit in the Big5 interpretations, namely that it is Better to be Extroverted, Better to be Open, Better to be Agreeable, Better to be Conscientious, and Better to be Not Neurotic, might be less present in data collected from nonjudgemental listeners, that is, therapists. Big5 is great for how you can use people. The very data of Big5 is judgements of others, and by the universality of Attribution Bias, it is morally judgemental judgement of others. So Big5 is not oriented toward what people are within themselves, and not great for how people can develop within themselves. In Big5, half of everyone is Bad in each of 5 dimensions; if they are truly independent dimensions then only 1 in 32 is (All) Good while 31 of 32 people are Bad in at least one way or another. Perhaps that's a Christian analysis in which people are (mostly) all sinners. But I wouldn't accept it in general, only for the limited context of how people can operationally or instrumentally make use of other people.
To conclude, I call for more research, studies of a particular kind, and I predict that that will demonstrate that Big5 while taking a step forward by adding Neuroticism, took a step backward into concrete-mindedness by collecting data in which the N/S dimension would be invisible, and perhaps using statistical methods which are not powered to find it.
Hopefully will emerge a Big Joint theory with 6 dimensions, which actually does represent an advance in scientific and practical insight, not just one step forward and another step back, and that will indeed capture the valid insights of previous theories.