It sort of depends on which incarnation of Celeron to which we're referring.
That said, you would, (as has been mentioned) need to install matching quantities of memory to even consider making a performance comparison. Win XP needs at least 1GB of RAM before it stops using the HDD page file as "available RAM" in all but the simplest tasks.
The 65nm Cedar Mill Celerons, (which were the last single cores introduced before a big change to dual core Celes) would pretty much take the measure of many P4s. Keep in mind these chips had very high clock speeds, and double the cache of the Prescott Celerons.
My personal experience with Prescott & Cedar Mill Celerons has been in comparison with a 3.06Ghz non-hyper threading 519 P4. I observed perhaps not even a 10% differential in performance between the CPUs. However, the Celes tend to "time out" a bit more when initializing large files or a Volume HDD, which is I suppose attributable to the smaller caches. My Cedar Mill 356 (3,33 GHz) was a dead heat with the P4.