The same recommendations pretty much hold true: Look for at least an HD4870 or GTX260. With either card you'll likely see double the framerate as you are with the HD3870. Also the AA performance with either card should be much better than the HD38700. Like my signature indicates, I have an HD3850 overclocked to near 3870 speeds. I just recently bought Assassin's Creed and it kills my card at 1280x1024. And when I enable AA (which I have to since the game's jaggies figuratively slice and dice my eyes), the performance hit is huge. Heck even Far Cry 2 plays a bit better, although I get bad mouse lag when the framerate drops below 30.
So if you do intend on picking up visually-demanding games every so often, and you would like to play them well, I do suggest getting the best card you can afford. At the time I bought my card, it played everything I had perfectly fine, maxed out, and with a smooth framerate. Now every game I add shows its weakness, especially with much needed AA. 1280x1024 on a 19" LCD just does not look good without AA.