You have to remember that Bruce Wayne isn't his actual personality. Rather, it's a mask that he's hiding so that people don't know that he's Batman. The polar opposites personality holds up incredibly well in Wayne's favor, hence it's safer to assume that Batman is the real Bruce Wayne. Though, I would argue that he still holds a weakness for women, so the playboy element is relatively true in many regards.
Looking through Black Panther's history, I'd say that I'm more than inclined to give BP the win if there's a hypothetical match-up between he and Batman.
http://marvel.wikia.com/T'Challa_(Earth-616)
Looking at this, Black Panther actually is a master of all known martial arts, which includes African and unknown fighting styles. The very idea that he's been groomed as a warrior as opposed as just a ninja, I would think would benefit Black Panther more in that regard. Combined with himself being embodied by the spirit of Bast, his powers increased to superhuman levels. He was able to kick Namor like a football hitting a field goal.
Aside from that, he's a master of weapons, marksmanship, expert tracker and hunter, master tactician and many other areas of interest.