I think one aspect which gets forgotten somewhat with the whole "competition" discussion is that gamer's tastes change over time as well.
Whole genres fade in and out of fashion. Niches with genres even more so. There's no doubt that the arena style shooter genre is far more smaller now than when Halo 3 released. That's not just because the titles releasing now are perceived to be of lower quality. There just isn't as much appetite for the style of game.
Halo 3 was obviously a good game. The fact that it was the most played title for three years running is a testament to that. The perceived drop in quality for the series since then has absolutely had a impact on its popularity. However, that's definitely not the only reason Halo's popularity has decreased.
Whole genres fade in and out of fashion. Niches with genres even more so. There's no doubt that the arena style shooter genre is far more smaller now than when Halo 3 released. That's not just because the titles releasing now are perceived to be of lower quality. There just isn't as much appetite for the style of game.
Halo 3 was obviously a good game. The fact that it was the most played title for three years running is a testament to that. The perceived drop in quality for the series since then has absolutely had a impact on its popularity. However, that's definitely not the only reason Halo's popularity has decreased.