It depends on the budget. Up until around the 2600+ level the AMD chips offer a better bang for the buck for sure. Above that, it's pretty much a wash.
As far as which CPU is faster, that's a topic for heated debate. They both have their strong points. There are very few areas in which one is a lot faster than the other. For gaming certainly, they are very evenly matched.
If you choose to go Intel, I'd recommend you go with an Intel i845PE chipset board (Asus P4PE as an example). The newer Granite Bay chipset seems to have unresolved fairly serious bugs in it when it comes to support for newer AGP 8x graphics cards. You should also be aware that the next Intel CPU to be released will not work on current motherboards. You should also really only be looking at the 'B' type P4s (533 MHz FSB parts). The 'A' type P4s are not very good performers.
If you choose to go with AMD I'd definately take a hard look at the nForce 2 chipset based boards. Some of these boards feature truely superb integrated sound which is unmatched by any standalone sound card in performance and features. (The Asus A7N8X Deluxe is the most popular motherboard in the enthusiast market right now. It has nearly everything you could want in a motherboard built on, except for graphics.) It is most definately worth the extra money to get the "deluxe" versions of nForce 2 boards with the full nForce 2 onboard sound option. ( Look at:
http://www6.tomshardware.com/game/20030405/index.html )
As far as CPUs go, for Intel, the 2.53 'B' is about the best for the price. For AMD, the 2400+ or 2500+ are very good as well. For a budget system, the 2100+ is a good choice.
(I rarely disagree with Skuzzy, but I'm not seeing any significant Intel lead with 9700 and 9800 pro benchmarks. The nForce 2 platform really helped AMD make up a lot of ground. Intel wins the Quake 3 benchmarks, 3dmark 2001 se is a tie, and AMD wins the Serious Sam 2 tests and UT 2003 tests. All others are pretty much a wash.
It's hard to find good reviews comparing the fastest Intel and AMD offer, but here's a small sample:
http://www.hardocp.com/article.html?art=NDI2LDQ= http://www.anandtech.com/cpu/showdoc.html?i=1783&p=12