nearly every Radeon will beat a Geforce 1 DDR, except the Radeon VE, when it comes to performance.
Power draw for Geforce 1 cards is fairly high (I heard 18 watts per chip), so you might want to think about that if you're running a Socket 7 system.
Finally feature wise, the Radeon series cards beats the Geforce 1 in nearly every way (I can't think of any that the GF wins, but I'm not about to say anything stupid).
you should consider a GF2 Pro if you are able to get your hands on it. Performance wise, it handily beats the Radeon in almost every situation, but feature wise, they're about the same (Radeon wins for hardware DVD acceleration of decoding).
just be sure when buying an nVidia based card that you know what you're doing when it comes to drivers, and 2D Quality (which could mean higher prices when looking for a specific card). AFAIK, there aren't any special issues with nVidia cards that require patches for the OS or anything, so they're typical in that area!
finally, when it comes to drivers, Radeon's are GREAT for Windows 9x, and pretty good for 2K (hasn't been a comparison in a while AFAIK, but it appears to me that they're doing well). XP drivers still don't exist I think, and Linux drivers for Radeon cards are too scarce for my tastes. nVidia drivers work around the whole PC, so basically you won't have to worry too much about drivers not being available for your OS.