If you are looking for a PIII, I would go for something that starts off at the 100MHz bus like the 700E. The main difference is that if you try to OC the 100MHz models, you can get higher without throwing your PCI devices too far out of spec (esp if you get around 133FSB).
On graphics performance, the AMD chips do slightly better on graphics applications (content creation benchmarks) although Intel does slightly better than the AMDs. Of course a lot of this depends on the chipset you are using, so the differences are pretty much negligible.
TBirds generally can OC better, but if you get the right PIII, those can be pushed pretty far as well. The difference is that OCIng the AMD chips does not stress the other components whereas OCing an Intel chip does (since AMD OCing is done by the multiplier). Valuewise, the AMD chips still win out. But since you already have a i815 board, the TBird isn't really an option.