I've handled/played and sold over 100 Schecters and have found them all to be of great quality especially for the money. IMO it's one of the best guitars out there in it's price range. The necks are nice, the pickups decent, the components are of decent quality, they're put together well, etc, etc, etc. Go to harmony Central and read the reviews. Last time I looked every review on the Schecters was great to outstanding. I don't think you'll be disappointed......
The C1 Classic has the SD JD and SD Jazz p'ups and the Exotic has the Super Rock's. I think the Super Rocks are going to be "dirtier" sounding than you want for jazz, but only your ears will know, not mine.
I recommend going to a store that carries them and playing them both. You'll get the answers to all of your questions best that way.