Can your motherboard support a 133MHz FSB? The Desktop PIII 1.13GHz is also a Tualatin, but cost 50% more than the Celeron 1.2GHz. Furthermore, it's still only 256k. But yes, it does perform better.
The server PIII 1.13GHz is a different version with 512KB cache and cost about 30% more than the desktop version, it's faster still.
If your motherboard can be pushed to 133MHz FSB, you might consider trying to overclock a Celeron 1.2GHz to 1.6GHz at that speed.
The use of any of these processors requires the Powerleap iP3/T adapter (and compatability with it, ask Powerleap). Furthermore, using the 133MHz bus on your motherboard, if available, requires PC133 memory and a recent enough video card to support the 89MHz AGP clock.
What's the frequency, Kenneth?