No, it's because you can't unstring a crossbow. Both are equally affected by the rain - string gets wet, fucks up the tension, have to wait for the string to dry out to use it again - but you can just take the string off a bow in a few seconds, coil it up, and pop it under your hat to keep it dry. As soon as the rain stops you restring the bow and you're good to go again, but the crossbows still need to dry out.

There was an additional complication for the Geonese in that something disrupted the supply lines and fucked up their 3-guys-per-2-crossbows tactic (one to fire, one to reload, and one to hold the shield they're all hiding behind), but I'd also consider that a point in the bows favour - all you need is the big stick, some little sticks, and a dry string.