West Coast & Dirty South are experimental with mainly electronic noises (808, 909, 707) and synths.
East Coast is generally experimental with all sounds, including electronic drums if the producer so feels. The drum patterns themselves are also a bit more experimented. It's basically the producer doing anything musically possible to make an ass shake. He'll put it a baby farting noise if he has to, and if it fits the beat. As long as it works.
My best advice would be to make beats. Just keep making beats, and after you're done making them, THEN separate them by which category they 'ended up' being. So when a vocalist approaches you and says "Gimme some hot dirty south", you don't have to come to futureproducers.com and ask "what are the basics for making a dirty south beat?" You'll already have an inventory of beats for the artist to choose from.