We know that no 2 persons are same So as a BA we should know that no 2 users will have same needs and even if they have they might not agree at that time. so whenever there is user conflict i suggest that meet the users seprately and make a note of their requirements and make them compromise the requiremnts and go by the priorities and the interests the the users and the organisation as a whole.
I think the best way to handle user conflicts is to document all the user requirements and send a copy to the user via email and ask for his sign off. This way you will have proof of what you (BA and User) initially agreed upon while gathering the requirements. So if at all user changes his word at the end you have the proof and you can show him what you initially agreed on.
