In the past I think NVidia cards may have done a bit better in that title, though I haven't seen a recent bench to say for sure. I will say though that you need a good processor to get decent frames in FSX. What is the rest of your system specs?
My system is an HP Pavillion with Intel Dual Core E5200(2.5 GHz,2MB L2,800MHz FSB) and 3GB DDR2-800MHz SDRAM. Graphics card is 512MB ATI Radeon HD 4350. I have not yet installed FSX but would expect the graphics card to be the bottleneck to decent performance.
If you still have the original 300watt PSU in there you are limited on options for GPU. Best I can recommend is GT240 which has performance on level with 9600GT but is power efficient. If you are ready to do a PSU upgrade as well the GTS250 would be a well matched card with your system. Then again there are some nice ATI solutions as well.
You will need to up that CPU to at least 3Ghz+ if you want playable frames....FSX is CPU dependant more than anything, and even though the game does not benfit from a quad core (uses 2 cores) the higher the clock the more frames you will get....