Board: A 4 5 7 J
Two players declare a low.
Player A: 3 4 x x
Player B: A 3 x x
Both players have the same low hand: A 3 4 5 7
Is this a tie or does Player B win with lower cards in his hand?
It's a tie. Win/loss is always dependent on 5 cards. The only times differences in hand cards matter is when determining who gets the extra chip(s) in a split pot. (Though some casinos go by position instead of hand cards for this.)