In absolutely no way do I want to imply that Halo 3's campaign is bad, it's great and I loved it, but for whatever reason Halo 3's best moments simply reminded me of moments I liked from Halo 1. Both games have Assault on the Control Room, a level where you have to run through tons of Flood in order to get the artifact that fires the Halo ring, a Warthog finale where you have to outrun a massive explosion. I'm sure I could think of a few more examples if I wasn't also busy at work right now.
The reason I like Halo 1 a little more over 3 is because 3 feels like it leans on "remember this from the first game?" a little too much. That, and while Halo 3 has some really memorable parts to it Halo 3 also has big parts of it I kind of forget existed while Halo 1 from start to finish feels memorable to me.