The Myers-Briggs is all about one singular mode of one's personality. For instance, you could be an executive or boss type under the MBTI name of ENTJ. Unfortunately, that's all you learn about them. The ideas behind the MBTI were hypothesized by Carl Jung in 1921 via a combination of intuition and logic. The personality types have not changed since then.
Under the Five Factor Model, you have fluid variables that you can fine tune to get a more specific understanding of a person. The Five Factor Model was originally compiled from a "lexical hypothesis" which says that if a personality trait is important, it will find its way into the language. They first researched this in 1936 by compiling thousands of words and then sorting them by synonyms (or close to synonym). Then, they went through tons and tons of personality test data, and they looked for which factors had the greatest predictability for the rest of the personality. In the 1940's, Raymond Cattell came up with 35 clusters and then 16 factors. In the 1960's, two Air Force researchers narrowed it to 5. From just 5, research shows the rest of the personality is fairly predictable. Cattrell disagreed with this due to its oversimplicity. In 1980, a peer review with 4 prominent researchers on the subject decided the FFM was the best personality test available. Nowadays, research shows that dumber people require less factors (such as maybe 4 or 5), while more intelligent people require maybe 7 or more variables to accurately predict their personality.
The bottomline is that this fluid approach by variables, which is backed up by tons and tons of research, is far superior to something a knucklehead came up with almost 100 years ago that no one has attempted to change.