If the graphics, hard disk size, and amount of memory are the same I would check if the Celeron is a Tualatin one. If it is get that. It runs cool, and it has 256K L2 cache. The S370 Celerons before it had 128K cache. The Athlon may have more Cache, but it think it will run hotter.
The CPU charts shows the Athlon at PC133 memory and the Celeron at PC100, so there will be a little difference in memory speed.
If the motherboard in the Celeron PC will run FSBs > 100 (if it will take a P3 it should) then you have an easy overclock. I ran a 1.2 Gig Celeron for a few years at 120 FSB, meaning the CPU was running at 1.44G. On a warm day with a basic/cheap cooler it would get to 35 - 38 C. If the memory in it is PC100 you may need to change it for PC133. Mine ran stable with cheap generic PC100 memory. Upping the FSB will reduce any difference down to mempory speed
The Tualatin Celeron was effectively a P3 Pentium, only with an FSB of 100 Meg instead of 133. The P3 and the Tualatin Celeron had the same amount of L2 Cache.
As the CPU charts show the Celeron is quicker than the Athlon and a 1.0 Gig P3, and thats running at 100 FSB.
Trying to overclock the Athlon would be more difficult as the FSB is already 133, and that is probably as far as the motherboard will go.
Rob.