Some here would probably hate me for that, but to be honest, I think Halo story was hardly as good as some like to paint in the games franchise. Halo CE story was pratically non-existent, Halo 2 was much better but again nothing fantastic (they explain more about the flood and the Halo rings at least), and Halo 3 came with that same thing again about destroying Halo to eliminate the Flood.
I do think the story used to be enough to justify the gameplay, but the story seems to be really deep only from outside sources, at least until Halo 3. From ODST maybe things started to change a bit, but it was 343 who actually added an extra sauce to it (even though that extra sauce wasn't exactly appreciated).
Gameplay wise Halo CE was fantastic, but when the Flood shows up it kind of goes downhill... it's good at the first levels they appear cause it changes the gameplay a bit, but it soon gets tiring. Changing the smart Elite AI to the smartless Flood from half the game to the end wasn't good. Halo 2 suffers from the same issue. Halo 3 managed to make the Flood much better than before, but it still shines when fighting brutes and Scarabs.
That said, I think that 343 gets way more hate then they deserve (but they still deserve a bit), while they're constantly compared to a Bungie that maybe never existed since improved by players nostalgia. Gameplay wise Halo 4 is far from perfect and I actually understand the criticism in the multiplayer aspect, but Halo 5 is the best multiplayer Halo game, and besides the story related issues the campaing is very good overall.
Edit: By the way, I first posted it quoting Vegetable Lasagna that said he prefer gameplay over story, but apparently he posted in the wrong thread. Still I didn't want to erase everything I wrote.