Actually, in benchmarks, the final generation of PIII's slightly overtake the original P4's. So, that's where they stand in relation to one another.
I had a PIII 800 system and installed an Asus MX4000 64mb video card, and it did fine, so I'm assuming it shouldn't be too big of a deal as long as you don't go overboard with the video card. I'll say it'll probably run just fine with a 6200 or something. Stay under the 6600 and 9800 line to not overstep your processor's capabilities.
<b>I'm an unhyphenated American.</b>
Intel Q6600 @ 3200 1.4v
Abit IP35 Pro "The Snake"
2x2gb A-Data @ 800
Diamond HD 3870 512mb
Great FORD TRUCK