McCoy presents to me what is perhaps the ideal representation of the Doctor. It’s either he or Troughton; they’re too similar. Of all the Doctors, these two are the most “clever”. They play (as Thom notes) the classic Shakespearian fool; their power lies mostly in subterfuge. In appearing stupid, or at least harmless, such as to disarm those around them and thereby to give them the upper hand.
To some extent or another, nearly every Doctor has had his tricks to this end. Hartnell just seems like a crabby old man. Davison is a wounded puppy dog. Tom Baker plays a very similar role to McCoy and Troughton, though through such a filter of mockery that you really don’t know what to make of him — thereby making him seem insane, and thereby, indirectly, probably not a threat. Though he’s erratic enough that maybe he shoots himself in the foot as often as not. Colin Baker seems like such a pompous ass that you dismiss him out of hand. McGann is so earnest, and keeps throwing out so much information that he shouldn’t know, that he’s either endearing or just plain batty — though I think more effectively than Tom Baker, in that at no point does McGann seem like a potential threat. Not sure what to say about Eccleston or Tennant.
The only Doctor who does not seem to possess this vital — and in my mind character-defining — quality is Pertwee, the “James Bond Doctor”, which probably accounts for his being my least favorite, despite his charm and warmth and whatnot. The other Doctors tend to get ranked according to the efficacity of their particular ruses.
And of all Doctors, I think McCoy and Troughton are both the easiest and most dangerous to underestimate.