I've recently downloaded the UT3 demo, and I must say, I'm more impressed than a lot of people have been. It runs relatively well for a demo, albeit with a few glaring bugs as always. The demo includes two Deathmatch maps, DM-Heatray and DM-Shangrila, and a Vehicle Capture the Flag map, vCTF-Suspense.
DM-heatray is a well-styled map and is familar from all the preview shots I've seen. It also includes a necris Darkwalker, a war-of-the-worlds like laser deathray gibbing machine. A vehicle in a deathmatch map? Strictly, when there are loads of players, it gets eaten alive by firepower as it's weapon isn't fast, but because it's so powerful, you can easily get killing sprees with it, no trouble.
DM-Shangrila is a map that reminds me of a similarly styled map from 04, masurao I think it was called. Oriental themed, and themed well. However, there's an inescapable graphical blur that stops me from ever feeling fully involved...
The VCTF mode is a real hoot, and the hoverboard is hilarious to use. Get shot and you fall off, and are a sitting duck from the artillery shells of a Hellfire, blasts from a Goliath, lasers from the Mantas and Raptors, or bombs from the new enhanced Scorpion. On the whole I really enjoyed it, apart from when a tem-mate caryying the flag decided to randomly walk of a cliff to his death, leaving me sweating.

Graphically, the game looks good. Unsurprisingly, it can be summed up by the simple equation of UT2004 + Gears of War = UT3, there or there abouts. Not that that's bad by any means.
On my system, I can get around 30-45fps in all games with the 'max detail settings' of the demo (I'm told this will equate to medium in the full game, uh oh) at a resolution of 1680x1050, which puts it in the same league as the other 'high requirements' games I have, Rainbow Six Vegas and Stalker. I prey it gets optimised a bit more, or it'll seem far less forgiving than it's 2004 counterpart.

Also, at a file size of 750MB it's quite small, so I thoroughly recommend you give it a look if you liked the old UT games, but make sure you have a decent PC first!