Steve,
Both the Sheraton and the later AS80/120 were made by Samick I believe. The Epi may be a slightly lower price point. Around $400+ while the Ibanez goes for $600+. There are some cosmetic differences. Opinions on the Epi seem to be good, but there is some dissatisfaction with the pickups. Many people change them out. With the Ibanez, you get the excellent Super 58 PUs. I'm not sure about the Epi neck profile, but I would think it is of the Gibson variety (thick from front to back, narrow from side to side). GC should have both guitars, so even if you cant get a feel for the sound, you can compare fit/finish and neck profiles.
If you're looking at Epi's, you might as well look at Yamahas and Washburns too. Both make excellent 335 copies.
If you want more opinions on the Epi, go to
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&group=rec.music.makers.guitar.jazz and do a search on Sheraton.
I have a Korean AS80 in butterscotch. 9.5/10. with OEM case. It is very pretty and well constructed. The action is low and it plays well. You want to buy it??? email me.