I'm not sure of any advantages that one may have over the other 2, but my personal preference would be soundmax because I haven't had any problems with it. Others have probably had different experiences with each one, so listen to their recommendations as well.
Realtek should be the best. Sound quality for all current onboard hd audio is about the same in term of noise ratio. Realtek has better driver support. When it gets old, you'll still be able to find working drivers for new os.
Reltek is by far the best for onboard audio. SoundMAX has a lot of background noise. I use it in my HP DC7800, it is pretty good when listening though speakers, but my headphones (BOSE quiet comfort 15) have a ton of background noise. I do not experience this when using Reltek. Also Reltek is used in motherboards for gaming and editing from top companies, For example ASUS (who are praised for the best onboard audio use Reltek). SoundMAX is used for HP DELL and others machines for businesses which audio is not needed as much!