Look at the benchmarks with AA enabled.
Ok. Last graph on the page:
5770: 8fps min, 14.28 max.
460: 7fps min, 14.99 max.
5850: 11fps min, 22.01 max.
The only playable frame rates with this title with ANY of these cards is at 1680x1050, 1xAA, where the 5850 takes the lead with the max frame rate (although at minimums equal to the 460). At 1920x1200 with 4xAA none of these cards have acceptable minimums, not even the 470. Which means in the one graph on the page where the 460 barely edges out the 5850 by one frame/second the settings aren't usable anyway.
Click on 'next' for bf:bc graphs and it's a total slaughter, not an arguable even match at unplayable settings.