New Graphics Card

There should be a $30-40 difference between those 2 cards you have in mind. Both are sufficient for your resolution. The HD 6870 is faster at stock speeds, the 460 overclocks much better.

For that resolution and budget consider the HD 5830 (runs hot but good performance for the price), HD 6850 and GTX 560 non-Ti (same price as the HD 6870).

Isn't the HD 6870 supposed to be 10 times faster than the HD 5830?

HD 5830 benchmarks- http://www.anandtech.com/bench/Product/171

HD 6870 benchmarks- http://www.anandtech.com/bench/Product/290

The 5830 should perform like the 6850. They were both intended to battle the GTX460. The 6850 is the better card as it uses less power. I'd get the 6870, more so if its the cheaper card.