I've been using ASAT for a couple of years now and really like it. I've used some predator as well, but the ASAT leafy suit seems to result in deer coming in closer - I had more deer in bow range last year than ever before - whether that's due to the ASAT or something else, I can't say.
My advice - buy just the ASAT leafy suit and wear that over your existing camo (or shorts, for that matter)