I have both systems, Intel and AMD. The AMD is a 761 chipset, the Intel is a 815EP chipset.
AMD board has faster memory performance, it really makes good use of DDR. It will be ready for the next generation cpu.
Intel cpu's run much cooler, heat is not an issue. It will not be able to upgrade to anything higher than a Tualatin overclocked at 1500MHz.
Both have equal stability, although I believe a novice will be able to set up the Intel easier. I do not have a P4 set up, but to get maximum performance the top of the line P4 cpu is priced way too high, when it performs roughly equal to the top of the line Athlon XP. AMD is priced considerably lower, and for $85 you can get a Tualeron 1GHz and run it 10 x 150 on a socket 370 board and get 1.9GHz P4 performance.
I play games mostly, so price per performance in games leads me to favor the AMD set up. This isn't to say you couldn't drop a big wad of money and overclock the new Northwood cpu to 2.5+GHz.