Always feed mice if they will take them...I've never had health problems, mice are easy to get, cheap, and not dangerous to the snake. I've never heard of a ball python eating anthing other than rodents in the wild. While many other snakes might, I seriously doubt balls eat anything other than rodents, primarily gerbils in the wild (yup I said it, gerbils in Africa...oh no, now someone is going to tell me the 100 or so species of gerbil in africa don't exist b/c their pet gerbils come from mongolia...lol).
Since I have never heard of anyone actually studying the benefits of varying a BPs diet, I assume that there are no such benefits...until someone proves me wrong (i.e. a long term study involving more than two snakes, I don't want to hear a bunch of people's anecdotes). All of my BPs have been just great with mice with maybe the occasional rat. In fact I think the less you vary your exact feeding procedure (food item, live or F/T, time of day, location, place where you buy you food items from etc...) the less likely you will have problems with them feeding in the future.