Polar bears would do wonderfully in the Antarctic. They would, however, devastate the seals and penguins that live there. Some penguin species such Adelie penguins are also doing poorly with changing Antarctic sea ice, but others like chinstrap penguins are doing very well.
Overall, polar bears need seal blubber for energy and there is lots of seal species in Antarctica. The seals and penguins are totally naive to surface predators and would likely be very easy prey (probably like ringed seals were when polar bears first evolved and moved onto the sea ice).
There is an international treaty that would preclude introduction of species to Antarctica so we'd have to change that. In general, conservation biologists don't move species to new areas where they don't already exist, because it often leads to more problems and new endangered species.