Yes you're right and with the reasoning too. Although king position will factor.
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I'm sure the answer to this will vary somewhat from game to game, but I'm wondering if there is a general principle here.
Let's say one side has a 2-1 pawn majority on one side of the board and the other side has a 3-2 or 4-3 pawn majority on the other side of the board and neither are very far advanced. Does one side typically have an advantage over the other? My thinking is that a 2-1 majority is better to have because it moves faster.
I face this situation frequently in games and have to decide whether to trade off the heavy pieces to get so a (mostly) pawn end game.