Omega Drivers are just ATI Catalyst drivers hacked so that a system with a mobile GPU will accept them without any trouble. They are slightly tweaked, too. I've never had any problems with Omega drivers, I'm on 4.1 now. As to which ones you want to use, the regular ATI drivers can be a pain to install on a mobile system, while Omega drivers come with a handy installation device. In fact, ATI comes very close to endorsing the Omega modded drivers. So, which ones you use are up to you. The problems with see-through ground in BF1942 haven't been resolved yet, so more drivers will be on the way, I'm sure.
This is just a general overview. If you search the forums you'll find a lot more information from a lot more knowledgeable people than me.