All my snares have a Remo Hazy Ambassador snare side...and the batter head is either Coated Emporer,Ebony Pinstripe,or Clear Emporer.I've found the Ebony gives off a Piccolo style sound but without being too high pitched.
Coated G1 is like the ambassador. I like a good ring coming from the snare, so I don't use dry heads or 2 ply heads. When the snare is a more open sound, it really fills the gaps when you solo or do ghost notes. Some people don't like ring at all, I love it.
I've got Aquarian Hi-Energy batter over a Classice Clear hazy reso on my snare and it sounds amazing with extreme durability. I love the sound with an emperor x but its pretty controlled and muffled, but the hi-energy is so open and so loud - really brings out the full sound in my Tico Torres sig snare(ultracast free floater) while keeping it durable enough to take a beating off me.
I tried an emporer on my old snare a long time ago when I was inexperienced and just assumed that an emporer would be better than an ambassador. It sounded pretty good from where I was sitting, but not to the listner. I didn't realize that it was choking the sound. Now I use a coated G1 batter and clear snare. I tune it low and let it ring out.
You cant go past the Remo CS dot heads for your snare. I love what they do to my steel ludgwig snare. The coated ambassadors are great too. I play rock/funk. Ive tried Aquarian and Evans when they're on special but keep coming back to Remo....