I always preferred the Halo 2 storyline just a little bit more
I did love Halo 2's storyline, but I'm not entirely sure I can say I preferred it to Halo 3.
Halo 2's seemed to not travel quite so far (Halo 2 has 15 missions, but that's because several larger missions are split into two, meaning we have more missions that effectively take place in the exact same location and really don't feel like a seperate mission at all).
And while I'm not one of the guys who hated the inclusion of the Arbiter, I can say that I enjoyed his pieces much less than the Master Chief missions (And I think this is a big, big reason why Halo 5's campaign was not as well recieved as any others, because we hardly get to play as the Chief. It would have been better had we either just played as Locke (as in ODST/Reach), or if we had had 75%+ of the game as Chief).
Halo 2 at times also felt like it's story was a little bit too similar to Halo CE, at least in having missions to explore another Halo, to (unwittingly) find/release a flood infestation, to locate an Index, and to infiltrate an enemy ship (well, space city).
But that's not to throw Halo 2 under the bus, since it's still a great game, highly enjoyable and replayable, and it is a good addition to the overall story.
But if I had to choose a favourite game from the core series, based on its storyline, I do think I would choose Halo 3. Combat Evolved is damned good too, but maybe there's something more fantastic about seeing the culmination of it all in Halo 3.