There is no much difference in a guy calling you babe or baby. However, a guy calling you babe is more of a guy flirting with you while, by him calling you baby is more intimate. A guy will call you baby if you two, are a couple.
I never liked being called "Babe" after watching the movie about a pig with the same name. Also being called baby makes me feel like a helpless infant. It really just depends on the person you are saying it to.