Yup. That was the Halo experience, Ocy. The anniversary edition only had a new coat of paint. Halo 2 is gonna feel a little less nicer to play tbh, but more than makes up for it in bombastic story.
Halo 3 probably strikes the best feel between 2's bombastic story, and 1's general goodness to feel. Backtracking is far more minimal in the later games as well.
Halo 4 is...different. Don't let that scare you away. It's focused on telling you a much more personal tale, to the point that actual bullets and action aren't even really the point.