Can't answer based on aerodynamics or biology, but consider that most insects have four wings. This includes the dragonflies, which are amazingly adept aerial predators. So clearly, at the insect size level, two wings don't seem to have a significant advantage over four.
The real problem, I think, is one of developmental biology. ALL vertebrates have the same basic skeletal plan, including four limbs. This is based on the function of low-level HOX genes. (Search elsewhere for details.) So if your 4-winged birds are going to have legs as well, they pretty well have to come from a lineage that split off in the very distant past, likely coeval with Earth's Cambrian. And you're also going to have a whole history that has 6-limbed vertebrates evolving in parallel with the 4-limbed ones.
Another possibility is that the hind limbs have become modified into wings too, so the critters somewhat resembled pterosaurs: http://pterosaur.net/flight.php
Edit: Just thought of a really neat example of convergent evolution producing a pair of very similar flying creatures, one (hummingbirds) a two-winged vertebrate, the other (hawk moths) a four-winged insect. From casual observation, there does not seem to be any great difference in flying ability. See e.g. http://en.wikipedia.org/wiki/Hyles_lineata and http://en.wikipedia.org/wiki/Macroglossum_stellatarum Note though that despite the similarities, there are also major differences, the most obvious external ones being 6 legs vs 2, and scales vs feathers.