The difference is the time particle '에' in the noun "예전". It makes the noun "예전" like an adverb. e.g. 예전 = 옛날 (both are nouns) 예전에 = 옛날에 (will be followed by "something happened") 아침 = the morning 아침에 = in the morning \^o^/

Simply put, 예전에 is used when describing something that happened sometime ago and 옛날 is for a very long time ago (ie back in the days...).