Yah, the SS II has a more asymetrical body. I also think they're different scale lengths. Pretty embarrased I don't know for sure, but someone here will know. Also, the SS1 has 3 PUPs vs 2--a single in the neck and a Humbucker in the bridge...
Good luck in your search. SS1s and even more so, SSIIs are pretty scarce on this side of the pond. I love my ebony/crown SSII, but she's not for sale right now...