Using the low quality settings even a GeForce 7300GS can happily play Company of Heroes at 1024x768. Everything else from the 6600GT upwards easily delivered playable performance at 1600x1200. As you can see, the Athlon64 3800+ processor was limiting performance at 132fps as this is where the 7600GT, 7800GT and 7950GT all topped out at 1024x768. The 7600GT actually did very well at 1600x1200, where it was just 8% slower than the 7800GT and 22% slower than the 7950GT.
The medium quality settings rubbed out the GeForce 7300GS as it managed just 35fps at 1024x768. The 6600GT performance at 1600x1200 was average, though it delivered very playable performance at 1280x1024. That said, the rest of the Nvidia field was able to deliver very playable performance at 1600x1200.
Now for the high quality settings which eliminates most of these Nvidia graphics cards. In fact only the 7800GT and 7950GT delivered playable performance and that was at 1024x768. Clearly in order to play this game in all its glory with a 7950GT for example, you are going to also require a processor with a lot more guts than the Athlon64 3800+. Of course the Athlon64 3800+ is no longer considered a powerful processor, but even so, at 2.40GHz this AMD processor is usually quite good in games.