I think it depends where they fight.

If polar bear would fight in the jungle it would get hot and go to drink water. At that time it would be completelly open for suplex from the gorilla.

And if they were to fight on the ice sheet the gorilla would not have any trees where to hang tire swing and he would get depressed and unintrested to fight. So in the end it boils down to what kind of social services and safety nets are in the arctic and can they help primates like 1989 released Belgian techno anthem Pump up the jam can help humans.

If you put them in the same room, whoever gets to set the climate control wins.

Say what you want this is is an interesting thought, although the polar bear would most likely win because of its sheer mass. The gorilla has a lot going for it. A silverback can get to almost half that weight and has a greater bite force, intelligence, agility, and reach. They can also throw punches of up to 2300 lbs of force, which could easily break a bone or skull.

Mountain gorillas are definitely not fat.

A more apt comparison would be a black bear vs a gorilla.