In my opinion you need an average frame rate of at least 60fps to have an enjoyable first person shooter experience. You may not share that opinion or perhaps you could play a more forgiving role given this card's intended market.
Anyway, as usual our first choice of gaming benchmark is the very demanding Crysis. Using the low visual settings, the Diamond Viper Radeon HD 3650 1GB managed 40fps at 1440x900. This may seem like an acceptable score for a non-gaming card but other products roughly in the same class like the GeForce 8600 GTS managed 63fps and even the old Radeon 2600 XT did better, rendering an average of 51fps. Meanwhile the slightly more expensive Radeon HD 3850 managed 82fps at 1920x1200.
Supreme Commander was not easy on the Radeon HD 3650 which struggled on resolutions higher than 1440x900 (we used medium visual quality settings), however this time it got to marginally beat both the GeForce 8600 GTS and the older Radeon 2600 XT.