This is a great, great question... that I suspect no-one can systematically answer :) Unless you have spent significant time working for or with all three, how can you truly compare?
FWIW, I only know BCG first hand, both as a client (pre-consulting) and a consultant. I have also worked with and for Bain and McK folks, but don't claim to know how they compare. BCG did build its early reputation on some theoretical models in the 60s and 70s ('BCG matrix' anyone?), but I doubt there is a significant difference in how BCGers approach a new problem vs. the other 2 guys anymore.
All three are outstanding companies, led by smart, passionate and competent managers and partners. They spend significant time and money trying to get better, so if an approach works better, that's what they will try first in the future. Still, my personal guess would be that the variance between individuals within a company would be greater than between companies. So if you have to chose which of MBB to join, make your decision based on location, industry strength or people you met, not based on reputation - either way, you can't really go wrong.