There are many differences between the two, of course. One of the systems was derived statistically and independently verified several times, while the other was not; one is empirical while the other is theoretical; one is trait-based, while the other is type-based; one is discussed in psychology texts, while the other is ignored. I'll leave it to one's imagination to determine which is which.
MBTI and Big Five are used for a variety of purposes, but they're both used for self-discovery, identification of learning styles, and so on. MBTI is suitable for these purposes, I guess, but there are better tools available. Ethically, if I'm going to be pigeonholed, it ought to be by a system that has some scientific backbone and actual validation behind it.