It depends upon your application, though. In what most Americans think of AWD as being good for, which is snow and terrible conditions like mud and ice, 4WD is far superior. But it's only meant to ever be used in such conditions. It allows you to climb up hills, go through a foot of snow, and so on. But it's part-time. You have to plan ahead. Most systems also can't be driven for long periods on pavement.
The military, the forest service, pretty much everyone who lives in Alaska, and so on, all use 4WD systems. It's for when you really are worried about getting stuck and it's hit the fan already.
AWD comes in two main varities. Full-time systems that are mostly good for rain, gravel/dirt roads, and dry pavement only, but that do improve handling considerably. But they aren't really designed for serious off-roading or extremely bad weather. Basically it's a lighter version of 4WD that's usable on any road surface/in engaged all of the time. Since this is what 90% of people are likely to encounter, it's a good compromise. Subaru is the best known example, though other fully-engaged AWD systems do exist (Mitsubishi EVO, and Audi Quattro as examples).
The other types are part-time AWD and are pretty much only good for getting you unstuck from snow and the like when you start your car in the morning. They react far too slowly to be of any real use on bad roads by themselves, and it's only with the addition of stability control and a lot of computing power that most of them keep from flying off the road in rain. These should, IMO, be avoided. Unfortunately, these make up 80-90% of the AWD market. People think that they are getting safety and bad-weather driving performance and in reality, they are getting pretty much nothing for their money other than maybe getting out of their driveway.