I've found, over time, that Enneagram, when taken seriously and given the time any well-thought out theory should be given, gives back more than the MBTI.
Enneagram is open-ended; MBTI is a straight-jacket.
I can easily spot my 5 sub-type, "Counter Type" but I test for several MBTI types: INTJ/INTP/INFJ/INFP and I've also tested ESTP and ENFP.
Beatrice Chestnut's book on Enneagram is awesome as are some of Riso/Hudson's books on Enneagram.
Reading the book, Cult of Personality Typing, Annie Murphy Paul writes about phrenology, astrology, MBTI, The Big Five and others, but she does not discuss, which means dismiss Enneagram which shows each type at its healthy, unhealthy and average state--and the movement which is natural for non-static beings, i.e. us humans.
MBTI was Isabel Briggs' "baby"; she was obsessed with it, and if you read the background for it, it's hard to take it seriously, which is good for me, because then I can "test" any type at all and not let it phase me:
Play with it; that's what it's good for as far as I've experienced it--going from ESTP (when I was 20ish/in the 80s) to INTJ for seven years (Humanmetrics site) and then the others.
We want quick reads, fixes, convenient labels. Enneagram doesn't give that--not if we go to the best sources and not breeze through it; it goes deeper than surface, "Wow, this is so me!"
Take the time and don't compare personality types, e.g. who would compare astrology to MBTI or phrenology to enneagram, really expecting to make "the best choice."