Both are damn nice cards.
If you want pure gaming performance then I'd lean towards the GF3 Ti500 as it is slightly faster in most cases, and nVidia's driver support is better... that said ATi has been making considerable strides in improving their drivers.
The R8500 has a better feature, and better DVD, and better FSAA in most cases, also you've got a guarantee of excellent 2D image quality which tends to be a weak point of many GF3's. You also get HydraVision and TV-Out with the R8500.
Either way your getting an excellent card, but if your only going to be doing "occasional gaming" as you state then I'd prefer the R8500 as it's a more well rounded card.
Having the extra money to spend on RDRAM if you go the route of the R8500 is always nice too.