Both your hands tie in points. If players have 2 pairs, it's only the higher pair that is used to break the tie. If that makes sense. He definitely had the better hand but it doesn't really matter what cards made up the lower scoring pair. And I think this is because if you start looking into the bottom pair scoring it could become very confusing.
For example what if one player had Q ,Q,J,J and the other had K,K,2,2. If you were to look at the bottom pair you could say that player one should win, or maybe they should tie because they both had one pair that was better then there opponents.
Because of this it's easier to just look at the Top pair and say that you two both had a pair of aces, and we'll as another pair