Whilst I would ultimately back the bear, one must not underestimate the tiger.
Cats have guile, cats have cunning and above all cats have a vicious streak which is not found in our bear cousins.
As said the polar bear has huge paws and will have an overall huge size advantage. However, I would argue a tigers teeth could get through the fat. If you put protection of their young in to the equation, the tiger would do even better. Although, all mammals (females) have a natural tendency to protect their offspring, the feline world do so with even greater passion.
So, just to summarise, the Polar bear will win but it would not be mincemeat as said.
Perhaps a better scrap would be a badger and a puma. Believe it or not, I would put my money on Bertie Badger.
Or a surreal scrap would be a Great White Shark and a Hippo.