The polar bear will take on male walruses, which is astounding.
In the bear vs tiger battle, it would probably fall within some range, like 65 / 35 percent one way or the other. I believe bears have an advantage because their front legs and paws are so powerful. The tiger, however, may be able to use this to his advantage, because tigers attack by clamping down on the throat. If the bear were to miss, the tiger may have access to the bear's trachea.