If you look at the heaven bench nVidia ran in DX11 with the 480 the card never falls below 32FPS the entire time @ 1920x1080. The 5870 dips below 20 at least 5 times. Sometimes we may be talking as low as 15FPS, hard to tell with the chart.
However on the other hand, if you ignore the heaven bench and look at DX11 titles currently out, you'll see something as weak as a 5830 can push them fine @ 1920x1080.
For me it's going to come down to how much faster the 480 is than a 5870 and of course, the asking price.