It depends on the games you will be playing, performance and setting expectations and of course power supply/cooling in your system.
The 7600GT has 12 pixel pipelines and 12 medium speed pixel shader pipelines.
The X1650 Pro has 4 pixel pipelines and 12 super-fast pixel shader pipelines.
Both cards suffer from reduced memory bandwidth as they both have only 128-bit memory interface.
In a nutshell, the X1650 Pro would be better at super shader-rich games like Oblivion or upcoming SM3.0/heavily pixel shader games.
The 7600GT will be better at older titles with light to medium shaders, as well as superior in games that use heavy bitmapped textures vs. shaders at all.
I've always recommended the X800GTO as it's a good compromise to the above but trades massive power for a few features.
X800GTO - 256-bit memory interface, 12-pixel pipelines, 12 high speed pixel shader pipelines. You can usually find one of these monsters for under $130 USD.
This is the best of both worlds, although it does NOT support Shader Model 3.0 (slightly nicer waters in Age of Empires III) nor FP16 blends for some forms of HDR (Source engines work great with HDR, but Oblivion, Splinter Cell and the latest Tomb Raider will disallow HDR without aftermarket patches/mods).
It'll play everything out there at high resolutions, massive AA/AF due to it's 256-bit memory interface. Moreover, some Sapphire models come with 16-pipelines (16 pixel/16 pixel shader!) if you're lucky, but don't count on that as it's not guaranteed. Even at 12 pixel/12 shader, 256-bit memory interface these things are monsters for every game out there for CHEAP.
Be aware though- they can generate a LOT of heat and suck a lot of power due to their memory controller, fat GPU and sheer speed. Make sure you have a 350-400W PSU and also good case cooling.