Give me both. Put the bivy in the hammock, and any bag you need in the bivvy. Gets you off the ground, keeps the wind and moisture out, and keeps you warm. You need a wind break if it's cold, but that's no biggy.

Although if I have to pick what to carry for space and weight, in most cases I'll bring a tarp and a few 55 gallon bags rather than the bivy and the tarp.