I've made this exact upgrade (Hercules brand GF2 MX to Gainward GFIII Ti200 GS).
I play only few types of games. Here is what I've seen:
MS Flight Sim 2002 (very much Processor dependent) - little improvement, but some
MS Motocross Madness 2 - big improvement
Quake III - huge improvement
3D Mark 2K and 2K1 (although not really games) - huge improvement
So, if you like Direct 3d games, you should se some to lots of improvement depending on your processor. If you like Open GL games, you should see lots of improvement.