Difficult to say for sure without knowing exacly which Celeron and P4 CPUs they are. Wikipedia claims that 2.2GHz Celerons can be either P4 architecture (I refuse to use that silly name Intel uses for that architecture) with 128KB cache (yuck!), Core with 512KB (not bad), or dual core with 512KB (nice!).
The Pentium 4 can be built on different processes and have either 256KB or 512KB cache. If it is the former, even the worst Celeron will have better performance and generate less heat (which is a huge problem with P4). If it is the latter, some software will run better with the Celeron, some with the P4. However, the Celeron, being fabbed on the same process with a higher frequency will probably be a lot hotter.