Suggest you go over to the Thompson Board and ask the guys there. They are dedicated Thompson freaks and will be in the position to analyze every nut, bolt and screw down to the metallurgical properties of the original iron ore that was mined to create the steel the gun was made of. (OK, a slight exaggeration, LOL.)
http://www.machinegunboards.com/forums/index.php?showforum=3
FWIW, it looks to me like a West Hurley 1928 that is being marketed by someone who doesn't know much about Thompsons. The "S" marked parts show that one of the previous owners dumped at least some of the West Hurley internal parts and replaced them with GI parts, which is a good thing. The seller describes the magazines as being 20 and 10-rounders, but unless they have all been altered, they look more like 30s and 20s.
You say you just want a "fun shooter", and this gun might be a good bet for you. Even if it doesn't run "grate" like the ad claims, it can be fixed. Since it has been sitting on GB for a while, you might want to contact the seller and see if they will accept a lower offer. The seller is a pawn shop, so they might not have much money into it. If they are NFA dealers, the first transfer to your FFL will not be taxed.
You say you prefer the looks of the M1/M1A1 to the 1928, but bear in mind that the 1928 will accept drums, while the M1 will not. A fifty-round drum dump will warm the cockles of anyone's heart. 100-round dumps are even better!