In most of the Korean grammar books, "yes" is basically translated as 네. On the other hand, people may use 예 in daily life conversations, especially in informal situations, possibly because of ease of pronunication. So, I personally expect that 네 is for more formal cases, while 예 is for more daily life informal cases. Nevertheless, it will be nice if there could be some native speakers to help us confirm (or rectify in case of mistakes) the above presumptions. Good day.