Ha, i was talking about this topic (animals of differing backgrounds fighting each other)with some guys at uni a few weeks back. It turns out that there's a show on some cable network (i think it's the discovery channel or something like that?) called
Animal Face Off.
Here's an interesting link to a game you can play with various animals (keep in mind there is 2 groups)
ANIMAL FACE OFF GAME
Anyway, by their simulation, they have the lion winning against a Brown Bear. THe lion would circle the bear until it got a chance to attack from behind. Anyway, they have some pretty good matchups on the site
Has anyone actually seen the show?