They’re both cold, they’re both icy and they’re both surrounding a pole. But Earth’s Arctic and the Antarctic are very different kinds of places. Most of the Arctic is sea ice, connected to surrounding land masses. Brown bears from northern hemisphere forests probably walked into the Arctic long ago. Over the eons, they adapted to their snowy surroundings, to become white polar bears.
Antarctica, on the other hand, is a land mass surrounded by an ocean. Penguins couldn’t have walked into Antarctica. It’s thought that ancestors of today’s penguins could fly. They might have flown to Antarctica. Penguins wouldn’t fare very well transplanted to the Arctic. That’s because they have very special requirements for feeding and breeding. Also, in Antarctica, partly because there are no bears, you can walk right up to a penguin. All their natural predators come from the sea. So, penguins in the Arctic would be very vulnerable to predators.
On the other hand, if you transplanted polar bears to Antarctica, there might be some denning problems for the female bears. But polar bears might do extremely well feeding on Antarctic penguins and seals that have never known a predator on land.