I came here originally because Darth Marsden at the Telltale Games forums (now at Double Fine; we all moved forums after TTG screwed theirs up) brought up Adywan's ANH:R in the middle of a communal rant on George Lucas.
By far my biggest issue with the SEs is Jedi Rocks, and ROTJ:DE fixes that. (Jedi Rocks > ROTJ Vader "No!" > Hayden ghost > CGI Jabba > Greedo shoots > CGI wampa).
I didn't care much for SW:DE 1.0 because the blockade runner had yellow walls and the dewback next to the cantina was purple, so I stuck with ANH:R for the first film instead. But since 2.1 came out, I watch the DEED. I think I only watch ANH:R sometimes because I already have it, since some of the changes sort of bother me (like making the Death Star explosion feel less epic than the Alderaan explosion.)
I mean, I /would/ have said that I'm not a stickler for the originals, but this is so unbelievably good that I take it back.
I only take issue with DJ's versions because they lack fine detail, comparatively.