Currently:
The newest Pentium 4's (Prescott):
Hottest P4 ever made, makes lots of heat and noise (Due to strong fan needed, more so when overclocking)
Need to have one at least 1ghz faster than an "equivolent" AMD processor for same performance.
No 64-bit capabilities (yet)
Can be overclocked but needs VERY efficient cooling solution.
Currently the only way to get PCI-e motherboards.
AMD's newest Athlon 64's (Socket 939):
Coolest running Athlon's ever, very good heat and can run with less powerful fans.. Very overclockable (Though again, you'll be on a powerful fan)
Built in memory controller, allows for better memory bandwidth and speed.
64-bit
No PCI-e yet... But this should be here in the next 2 months.
Top of the line AMD chip: $850 (roughly)
Top of the line P4 chip: $999 (roughly)
Which wins the benchmarks? AMD.
In general, AMD's cost $50 to $100 less than P4s of equivolent performance. Traditionally (As in, has been the case for the past 4 years), AMD chips run 66% as fast as Intel (2ghz vs 3ghz) but have the same performance.
My vote is AMD