Some string materials are quieter than others. Heavier arrows will reduce the noise of just about any bow, and you can make your carbons just as heavy as your woodies if you want to.
Regardless, I've always found recurves to be louder than longbows. They have string contact with the limbs, i.e., the recurved part of the limb tip, that longbows don't have. The string slapping the belly side of the recurve makes extra noise. It can be reduced by wrapping the string in that area with wool and/or placing mole skin or some other soft material in the string groove, but the additional noise cannot be completely eliminated.