Neutering means that cats don't make such good mousers. Neutering does not affect a cat's ability to catch mice. It is cruel to neuter a cat. Your male cat will be less likely to wander and get in to fights and therefore less likely to pick up infection and disease. A female neutered cat will be in better condition with no hungry litters to feed, and less likely to contract certain diseases.
Neutered cats get fat.
Your cat will only put on weight if you over feed it. A neutered cat will stay trim with a normal, balanced diet.