I envision this bout happening in a half water, half dry Astroturf venue.
If it were a shark vs a grizzly bear (there was a novel written about guys trying to do a reality cable show on that very theme) the battle would go to whomever dragged the other to its own element- sharks are exclusively aquatic, and grizzly bears are land predators.
Both polar bears and crocodiles are somewhat amphibious in behavior. So it might be a more interesting fight.
The crocodile is better at holding its breath underwater though. And has thick skin. It would have to grab the bear with its long jaws, and hold the bear under water. The bear would try to maneuver around to get on the crocodiles back to plant his teeth in the croc's neck. Am thinking that the crocodile would have the edge. But it wouldn't be a sure thing.