Either processor can be a good choice. If you decide to get a P4 I would definately make sure it's the newer Northwood type. The following are my opinions assuming you are not contemplating overclocking..
Athlon advantages
1. less expensive by about $50
2. small advantage in the majority of benchmarks
disadvantages
1. fairly easy to chip processor during assembly if not careful
2. needs a bit more cooling which means it potentially can make for a louder system
3. if used with a Via motherboard it might require slightly more maintenance in terms of updating 4in1 drivers, but this is not the hassle it used to be so not really a big deal.
P4 advantages
1. Northwood runs cooler so system can be a bit quieter if designed for that purpose.
2. small advantage in a few benchmarks. If used with RDRAM does even better
3. on chip thermal protection
4. if used with an Intel chipset has a very high reputation for stability which is probably at least partially deserved.
5. retail version is very easy to assemble and comes with a nice HSF which is very quiet.
6. has additional instruction set SSE2 which can increase performance with applications designed to use these instructions
disadvantages
1. more expensive
Out of all this there are three things that I think really matter, performance isn't one of them because in the real world either one will perform very well.
1. If you're building it yourself assembling the HSF to the cpu on the Athlon is not that difficult, but it's a lot more difficult than doing the same thing with the P4.
2. Overall system noise. With a P4 system the power supply fans and case fans and hard drive are probably going to be the loudest things, so by using quieter ones you can end up with a very quiet system. The standard Athlon HSF is not especially noisy but some of the aftermarket HSFs are very noisy.
3. Money. P4s are better deals than they used to be but Athlons still have an edge.
Now if you are interested in overclocking the whole picture changes..