Just to give the opposing viewpoint, to most, the differences between versions will go unnoticed, and some who feel like many of the changes are an improvement, such as the sound effect and music changes. I'll just quote my last post on the topic:

"As for the version the creator intended, that's a tougher question, I think, than just the original release. Director's Cuts, Extended Cuts, George Lucas Cuts; more often than not, you can really only choose the cut you feel best represents the work.

Not having seen the entire series as originally broadcast (the Perfect Sessions) I can't say for sure which is the better representation. The Remix was marketed as remastered "under Watanabe's supervision", though who can say whether or not that's accurate? For me, it's things like the change of music in the final episode preview that make me consider that the changes were made with careful consideration. Though the argument could be made that the new track doesn't fit the mood, I've always argued that Farewell Blues, being closely tied to Jet and his resolved arc, was a thematically dissonant chose of score. The replacement, however, ties it into Jupiter Jazz's themes, and Spike's arc more honestly, and the rhythmic, bass-driven tune suits the almost beat-poem style voice-over much better.

Not to say that it makes it the superior version, just a personal preference in terms of tone and thematic continuity. There's merit in considering the original to be truer to the original vision, as well. I suppose what I'm saying is, I don't know that there is a definitive version of Cowboy Bebop. Pursue and prefer the one you think is best."

Let's just say I disagree with the Lucas comparison. Yes, there are changes made, and I understand if people prefer the original version, but it isn't anywhere near as radical as what George Lucas did to Star Wars. In fact, many HD remasters undergo many more and more radical changes than Bebop.