Thanks for the replies. I really hate it when companies release significantly different versions of a game under the same title with nothing to really tell them apart.
I actually have a copy of the Collector's Series, although I never got around to playing it. I bought it thinking that it was just a Windows port of the original games, but then I read the reviews which said that they changed more than just the engine. Like leaving out some cutscenes, not upgrading others, doing away with the interactive music, etc. So I decided that I wanted to play the originals, but my old system wasn't fast enough to run most stuff in DOSBox and even though it was Win98SE, my success rate at running DOS games was about 50/50.
Now I have a much faster system and would like to try playing these games. I just need to make sure that I get the right ones. I'm pretty sure that I have one of them already. Many years ago, I bought a combo pack of Lucasarts games which included the Rebel Alliance games, one of the Collector's CD-ROMs and a demo version of Dark Forces (which the eBay listing neglected to mention wasn't the full game). I need to dig it out and see which one I have.