I think that most (if not all) of the people reading this know about Halo: Combat Evolved Anniversary, for those who don't, here a short synopsis: Halo: Combat Evolved Anniversary, Halo CEA for short, is a so-called 'visual remake' released in 2011. CEA was supposed to be the way the game should have looked, if the makers of the game (Bungie) were capable of it at the time. The CEA engine is identical to the original version, this also allowed the developers to be able to switch between the two visual styles at the press of a button. But besides the look of the campaign, there is no difference, except a few hidden easter eggs. The multiplayer and forge part of it is completely separate from the CEA engine and cannot be seen as part of the game, more of an add-on to the overall package.
I think that if we get more Anniversary Editions from previous games, they should do it differently than CEA. For one thing, they should look to the Pokémon games Pokémon FireRed and LeafGreen and Pokémon HeartGold and SoulSilver. Although very different in game format, they too have made remakes of previous successful games, but they did it completely differently. Instead of upgrading just the graphics, they have implemented much needed upgrades that were designed for games that came after the original, without sacrificing the nostalgic aspect of the game. Translated into Halo, this would mean that the Anniversary Edition should have an implemented Sprint option, something that was added in Halo: Reach but expanded upon in Halo 4. But not only in gameplay, but also in backstory. If Halo 2 Anniversary became reality, I would hope they would expand the story. Keep the main story intact as it is, but try to fit in other campaign stories in it as well. We have a lot of canon to fit into that timeframe, maybe follow the timeline of 2552's September Anomaly in a secondary campaign?
But will 343i, if they make more Anniversary editions, do all this? I sure hope so, but I doubt it. Not only is it very costly to make all of this, considering all parts of development, they need to be able to sell it. Halo 4 may be loaded with canonical facts from the books, they may choose to keep things a little lighter in the rest of the games.