Surprisingly, the PIII's were more poweful, "pound for pound" than the PIV's. They changed designs mainly because of heat dissipation issues.
With that in mind, I'd be willing to wager a PIII 1.13Ghz would go toe-to-toe with an Athlon 1.2Ghz or perhaps even the 1.4.
I don't have benchmarks to prove it though, just an educated guess. Or the ramblings of an old man. Could go either way.