While Library compensates for the loss of handsize by letting you draw back to 7, Counting House lets you discard your Coppers knowing you can safely draw them back into your hand.  This is especially valuable in situations where you might want to save a Curse or other bad card in your hand in case you are then hit by Mountebank (to discard it) or Bishop (to trash it).

Of course, this works just as well against Goons, and possibly even better against Torturer (allowing you to discard up to 4 Coppers if you have the Counting House in hand).  But it gets completely wrecked by Ghost Ship, unless you’re willing to put your Counting House back on the deck.