That picture looks really washed out and stretched compared to this
http://screenshots.teamxbox.com/screen/31072/Halo-2/
As for comparisons, Scoob's super HD pick obviously is too hi-rez, but I noticed most of the Halo 2 screens you guys are picking out are MP. I have not played a ton of Halo/Halo 2, but from what I have seen the SP graphics frequently look a lot better (probably because MP has to account for possibly 4 people on 1 TV in 4-way split screen). I don't have Halo 2 or an Xbox and no screen capture stuff, and there seems to be limited in-game direct feed shots, but here are some examples that look significantly btw imo than the MP shots being shown.
http://screenshots.teamxbox.com/screen/31080/Halo-2/
http://screenshots.teamxbox.com/screen/31106/Halo-2/
http://screenshots.teamxbox.com/screen/31107/Halo-2/
http://screenshots.teamxbox.com/screen/31086/Halo-2/
As for past Halo 2 demos, Bungie did explain that. They were aiming for stencil shadows (ala Chronicles of Riddick and Doom 3, both of which did this on the Xbox) but it did not work out so it was cut. The 2003 footage was rendered the same technique Heavenly Sword used in 2005: In-game engine and assets weaved together post-process.
The Halo 3 trailer was shown to be in realtime and working to a number of game journalists and in the recent video. To lump it in with the Halo 2 2003 footage, which they admitted was not realtime, is kind of stretching it. True, the finalized game may have far too much on screen to maintain the quality shown in the trailer. Or vice versa, with 12-18 months of development they may add features (as they indicated at E3). All we know is it is in-engine, and the camera can be moved, ditto the player, which is a step up from a cut-scene with a very fixed camera to cover up all the flaws and engine problems.
But the jury will remain out until we see actual gameplay... just like every other game. But like I posted before E3, Bungie's strengths are more AI and game design and story imo. The fact their MC looks a LOT better than the DoA4 Spartan *and* has more effects (like self shadowing) is very impressive. Hopefully since they are using content cut from Halo 2 and have a 3 year dev window and more staff Halo 3 will be what people had hoped Halo was and wished Halo 2 would be.