I've played the S1 and S2. Fantastic guitars - very refined, superb build quality, sound great. I was on a Strat-quest recently and tried many Fenders and Suhrs. The S1 and S2 were better than any of the Fenders I tried, including a couple of Custom Shop models. I preferred the S1 (rosewood board) to the S2 (maple).
However, I ended up going the extra mile and buying a Suhr Standard. Best guitar I've ever owned. Just fantastic.
A couple of points to bear in mind:
Wouldn't you want a humbucker in the neck for jazz?
The necks on most Suhrs are quite thin. Suits me fine, but those liking a chunkier neck might be disappointed.