When it comes down to performance, Aliens vs. Predator is happiest in DirectX 11 mode running on a card with ample performance. That means you'll want at least a Radeon HD 5770 for 1920x1080 and at least a Radeon HD 5850 at 2560x1600. If you want to use 4xAA, 1920x1080 is a realistic cap, and a Radeon HD 5850 is the minimum you'll need for that setting.
That's not to say that DirectX 9 mode delivers sub-par visuals. In fact, it's almost impossible to see the difference. However, in this particular game, the DirectX 11 code path offers higher frame rates and has a monopoly on AA. Those features are important enough to get the DirectX 11 option a solid recommendation.
With texture memory lowered to the normal setting, lesser cards with 512MB like the Radeon HD 5670 can hit modest frame rates at 1280x1024, and the GeForce 9800 GT can handle 1650x1080.
If you're in possession of something with a little less power, you're going to need to lower other settings in order to get a smooth minimum frame rate. Unfortunately, AA is not an option for folks with powerful DirectX 9- or 10-class graphics cards. Even though your system might have the rendering muscle to spare, cleaning lower resolutions up with some AA isn't an option for anything but a DirectX 11 card.
How about the gameplay? I've been quite hard on Aliens vs. Predator, a game that I'll admit is an enjoyable diversion. I will say that the developers really nailed the spirit of the license through the use of shadows and lighting, providing a rich environment for both aliens and predators to stalk. No doubt marines will be doing a lot of nail biting. The aliens are particularly well-rendered, and it's hard not to be unsettled by the way they look when approaching you down a dimly-lit corridor. For a lot of people (myself included) the good parts of Aliens vs. Predator might be enough to keep you playing the three relatively short single-player campaigns, especially if you're a fan of the license.
On the downside, it always hurts more to see a game that does so much right while missing a few key fundamentals that could have launched it to greatness. For me, the hand-holding and oversimplification of the single-player game, combined with some underwhelming and obviously corral-inspired level design, really prevented me from enjoying this title as much as I wanted to. At least that's where I'm throwing the blame. When I asked some friends why the classic version seemed better, all they could say was that it was more fun. Maybe that's the best way to put it. Multiplayer modes provide some good times, but even that aspect of the game is tarnished with relatively slow matchmaking.
To summarize, I'm enjoying Aliens vs. Predator enough to play through the marine campaign, I'll probably play through the predator campaign, and I just might play through the alien campaign. While the new game doesn't raise the bar like Rebellion's original did, it does make great use of the license. The multiplayer options can also be fun, but unfortunately the uninspired single-player levels and dumbed-down gameplay leave me wondering how much better the new Aliens vs. Predator could have been.