Bungie went to great lengths to improve upon the graphics engine inside of Halo: Reach. While the game may feature many of the same elements (Warthogs, Covenant, and the trusty assault rifle), they've all been heavily augmented. In comparison to the original Halo 3 engine, the new Reach engine handles many more light sources and has higher-resolution textures wrapped onto models with considerably greater polygon counts. Almost all the art was remade, with influence coming from the concept art generated for the original Halo.
We went through Halo: Reach to gather a smattering of examples. Seeing as just about everything has indeed changed, it's far from comprehensive. Of particular note, the boost in antialiasing does a great deal to clean up the look of the game overall.
Guns are a big part of the Halo universe--you're always firing one, and it's the one thing that comes with you from scene to scene. The now iconic assault rifle features more intricate detail, and a smaller readout to match. Reach's DMR is considerably cleaner than Halo 3's Battle Rifle, with fewer jagged lines marring the look and a much more rounded scope, among other changes. Halo 3's Needler looks downright flamboyant when compared to the Spartan look of the Reach model. Bungie ditched the shiny purple exterior and upped the ante on the needles.
DMR / Battle Rifle
The Reach vehicles seem to have been simplified considerably. The Warthog no longer has wheels that match its exterior, and the Scorpion tank looks cleaner without all the jagged edges, hand holds, and exhaust vents. The Mongoose no longer looks like a mini-Warthog and takes on a more ATV-like look. Bungie also gave the Ghost a major revamp, which is evident just by looking at the cannons--the Halo 3 version is a blurry mess by comparison.
Reach's trees and outdoor environments look fantastic, and the developers went to great lengths to show them off in the campaign.
Bungie gave a lot of love to the Covenant Grunt. The tiny Bumblebee look-alike now sports a massive headdress and refined armor, making it about as menacing as a Grunt can get. Until it meets your elbow, that is.