Meaning is absolutely same, but どうして is more polite than なんで. We don't say なんで to teacher or respect people. Young people usually say なんでーto friend.

どうして　and なんで　are same meanig. But I never say どうして　and 　なんで to respected people. Becuse they are both colloquial style. I say どうしてですか　or なんでですか　to them. They are very polite expression. I think you had better only use どうしてですか　or なんでですか　except your friend. Please don't forget it.