A .303 with 215g would do for leopard and I would think the .303 has been used for years in Canada on bears. I would think the lightest calibre you would have to use the heaviest projectile. I think polar bears would be a tough animal but I saw a documentary years ago and natives where using a Winchester 94 in .30/30 on a polar bear but took 3 shots to down it. I would go for a .375H&H minimum on these bears.

steve