These 'either/or' threads are interesting, but tough! As every drum brand has professional endorsers who play jazz, funk, alt rock, fusion and gospel on the same kit I think it's hard to make the claim that any one kit is exclusively better for a certain genre - rock drummers play Gretsch, Jazz drummers play Yamaha Maple's, Fusion drummers play Mapex Saturns, etc...) A few months ago no one would have put Ludwig and fusion in the same sentence, but now Vinnie's moved over, have they suddenly become the ultimate fusion kit?
In the price bracket you are considering every brand has a kit that will do the job.The big factor for playing in specific genres is the head choice and tuning. I would have thought that most modern high-end kits are going to tune throughout the sort of tuning range you are after.
There's so much choice, there's nothing wrong about cutting down the choice to USA Custom or Collector's Series if there's something about the sound or the brands that you like. However, DW collectors and Gretsch sound very very different from each other so the big question is, which sound do you prefer?
If you like them both equally, then ask yourself which do you think looks nicer?
Which is better priced?
Which brand turns you on more?
Do you want to say you are a DW player or a Gretsch player?
These might sound shallow, but if you can't decide on sound, decide on looks!!
I own a Gretsch now, but have owned DW Collectors before. I prefer the Gretsch (but I've always preferred the sound of a straight sided shell). It is a much more 'alive' sounding kit than a DW to me. The DW sounded a bit dull and thuddy - like a very good drum machine, but I suppose you could argue that that generic 'studio' sound makes it versatile. If you want a Gretsch to be thuddy and DW-like you can throw some EC2s on it, but there's no head out there that can make a DW sound like a Gretsch. I've always found DW collectors to be a big let down, but others love them... as you only have to do a quick search on here to see.
Maybe look at Yamaha Maple Customs too if you want another good all-rounder in the mix.
Size wise, 10, 12, 14, 16 makes sense, but do consider a 20" bass drum. If you are mainly interested in jazz, funk, fusion there's no reason why you need to go bigger (you can get a good 20" bass drum to rock hard as well)
Good luck!