Well, I got the 1000 for Anniversary so I think it's time to post some thoughts.
First of all, there are a couple of things about CE that I love that were never properly replicated in the later games. It's so refreshing having a crosshair in the middle of the screen oh man, every other Halo having a lowered crosshair throws me off so bad considering every other FPS game in existence ever of all time keeps it centered. I also miss how much of a spectacle it was shooting the AR, and even the pistol to a lesser extent. The particle effects from shots hitting walls, and the blood gushing out of Grunts while you shot them up is so nice, it was never really properly replicated since and it looks great seeing how it appears in the new graphical layer, and the sound, the AR has never been as fun to use as it was in CE.
The game is also snappy in its controls. The inclusion of Bumper Jumper was great because it brings the perfect Halo control scheme to the best game in the series. Playing through it again just reminds me how responsive everything is, mostly in the item interactions. You don't have to hold use to pick up health, you just... walk to it, how novel a concept is that. You go into a vehicle at the tap of a button, no half-second hold necessary. I like that the health has no regeneration of its own, and that health packs don't inexplicably make my shields charge instantly.
Now, speaking to the new graphical layer. It is gorgeous, it's like a Craig Mullins piece in playable form. I remember my impression from the original trailer, and seeing the general art interpretation differences in the environments, the derpy Master Chief model, and the PTSD from seeing Reach's AR made me want to write off the new visuals all together, but using them for skull and terminal hunting made me never want to go back to the classic. I thought I'd hate the artistic licensing they'd use with redesigning the look of areas, but when directly comparing them to the old look, most of the old stuff is just very dark and sterile. Even in comparison to Reach, this game looks so refreshing, the colours, the vibrancy of the environment, this is what Halo is. Just looking at Installation 04 Firefight map with that part of the game in Anniversary, and Anniversary shames it. Shove that Reach crap under the carpet and forget about it forever.
Reach, even a year later it's still disappointing me. I'm talking about the multiplayer, and for a number of possible reasons that concluded it being necessary to use Reach as its base, just sucks and does a 10 year Anniversary to the experience that brought life to the Xbox a huge disservice. Try as hard as you might to try and bandage that game's settings into something salvageable I am just so sick and tired of everything surrounding Reach. I don't like hearing its title music, I don't like its grainy ugly look, I don't like the way it plays, I just want it gone and I'm done with it. As far as I'm concerned that part doesn't even exist in Anniversary.
As for the music and sound, I thought the new music was good. Very subtle for the most part and still retains the greatness of the original. All except for my favourite track On a Pale Horse where it ends up sounding worse. Maybe I'm just more picky with it because it holds a strong nostalgic memory for me, and the new version doesn't do it justice. Other than that, it's great. New sounds took some getting used to, but I like them overall. Though the lack of classic sounds also discourages me to play in classic mode at all.
Now some other brief nitpicks/thoughts:
-I always liked the Elite Minor look, so now that they changed up their appearances to match the rest of the games, I think it's a bit of a shame. The sword Elite cutscene in Silent Cartographer looks so weird now because he's so chunky, hah.
-Super nitpick but I think the crosshairs for the Warthog are kinda rough. Both for the turret and the navigational arrow. For that matter, the flashlight indicator is pretty janky too. Also as has been covered by others, huge sniper rifle crosshair.
-Some visual feedback is less effective in the new graphical layer. There's no flash for pistol shots registering, the shields on Elites are not very clear, and at times I have trouble catching where a plasma grenade goes or sticks.
-This one is SUUUPER nitpicky but I always liked this graphic in the original so screw it. The new bullet decal for metal surfaces looks bad. It looks like I'm punching a hole through paper. All the other ones are good though.
-The plasma turret shots are a bit blown out in Anniversary, they're big and distracting.
-Rockets look weird in motion, there's I can't see a rocket, just a moving flare.
-I love just about everything about the new look for the environments except for one niggling detail. The Forerunner doors. Specifically the sliding doors in AotCR for the bridges and the big ones before the control room. They look terrible, and to make it even worse they seem to exhibit the most problematic case of texture stream-in. They don't look good at their best, but they're usually blurry on top of that.
-The water is fantastic. So are the skyboxes.
Anyhoo, I think that's about everything I have to say about Anniversary from my experience with it. Playing through the campaign again with the new visual layer has been great, and trying out the skulls has made it new again. Grunt Funeral + Boom is ridiculous. A shame that Grunt Funeral is a first run exclusive, because I think it's the best one in terms of changing up how things play.