In Halo 1's case, the anniversary graphics are garish and horrible, so most players looking to replay it will avoid it entirely.
For Halo 2, the Anniversary graphics are mostly tasteful and truer to the original art style, however the previously in game cut scenes have been replaced by full CGI reproductions that change the tone, pacing and feel of the story, and all the music has been re-recorded and, in some cases, replaced entirely with inferior music.
So in Halo 2's case there has never really been a comfortable mode in which people can be completely satisfied. You were either stuck with an inferior classic version of both 1 and 2, or stuck with two versions of the game which change far too much to truly feel like their original identity is intact.
I'd argue both cases are worse than what occurred in the re-release of the Star Wars trilogy.
Personally, the ideal Halo 2 would be Anniversary graphics, Classic music, and Classic cutscenes with Anniversary models.