Bear would win easy - for one thing, gorillas generally are herbivores and don't fight much, for another, polar bears are much much bigger as has been pointed out.
Now, say you replaced your gorilla with a rhino - now you're talking a more even match up! On the plus side, a rhino weighs a ton or more, so the bear is at a bit of a disadvantage there, and the rhino does have a very thick hide. The bear still has claws, and is much more agile as well, so it'd be one mother of a fight.
I wonder if the Romans - who used to fight animals against each other in the colloseum as well as humans vs humans and humans vs animals - ever fought a brown/black bear against a rhino? (interlude while I google) Hmm, nothing definitive, but this guy thinks waaaaaaaayyyyyy too much about who would win a lion-tiger fight:
http://indrajit.wordpress.com/category/lion-vs-tiger/