It does happen in both BUT it tends to happen ALOT less often with Rats. As Janine said, it usually only happens when its a first litter or when the animals are not getting enough protein in their diet.
Breeding mice vs rats depends on your personal needs. I am currently breeding both (but more mice than rats) as I have very small corns as well as near adults. A word of warning though, some corns will NOT eat rats unless they have been introduced to the "rattie" smell from when they are young (ie, from when they are big enough to eat rat pinks). My adult corn flat out refuses to eat rats in any form! Even live and I know that a friend of mine has the same problems with his corns.