1. Intel or AMD?
This is what you'll want to ask yourself before building anything. It'll determine performance orientation as well as motherboard, RAM and PSU choice.
I. Single-core
The general rule of thumb for single-core chips (Pentium 4 and Athlon 64) is the following: Intel for audio/video encoding, heavy multitasking, some 3D rendering; AMD for everything else - especially games, compilers, scientific apps, video editing, and some other 3D rendering. The respective leads in each area are quite significant, so going with a P4 system for gaming or an A64 system for A/V encoding is just a bad idea.
Things get a little more complicated when you switch to 64-bit. All Athlon 64s are 64-bit, but only Intel's Pentium 4 6xx and 5x1 chips are (so a P4 630 or 531 is 64-bit, but not a 530). The 6xx P4s are basically 5x1 P4s with twice the cache, however they're not really any faster since their cache runs slower. Also keep in mind that Athlon 64s run 64-bit code faster than equivalent P4s, so I suggest taking a good look at some benchmarks before considering a P4 for a 64-bit system.
Note that you do not need a 64-bit OS for an Athlon 64 or 64-bit Pentium. Both chips execute 32-bit code natively with no performance hit, and they will work just great with your old copy of Windows XP.
Finally, Intel desktop processors draw quite a bit more power than AMD ones, due to a number of reasons (mainly high transistor count and power leakage). Power consumption figures for Intel and AMD systems can be found here. As the chart shows, a mid-range P4 system can draw between 50 and 80W more than an equivalent A64 system, which translates to greater heat dissipation and a need for better cooling.
II. Dual-core
AMD's dual-core chips (Athlon 64 X2) are faster than Intel's (Pentium D) in pretty much everything, even A/V encoding. This comes at a price, however, as the cheapest A64 X2 is still around $100 more expensive than the cheapest P-D. Performance does follow, however, as A64 X2s have the performance advantage over Pentium Ds at the same price points.
Athlon 64 X2 chips work in most existing Socket 939 boards (except VIA K8T890 ones) with just a BIOS update. On the Intel side, the Pentium D requires a new motherboard with an Intel 945, Intel 955X, or nForce 4 Intel Edition chipset. This means that if you already have an LGA775 Pentium 4 system, you'll almost definitely need a new motherboard to be able to use a Pentium D. The same goes for AMD systems with VIA K8T890 chipsets.
Regarding power consumption, the picture is the same as with single-core chips: the Pentium D 840, for instance, draws over 100W more at full load than its A64 X2 equivalent (the 4200+). You would therefore be ill advised to go with a Pentium D if you intend on building a quiet system.
Lastly, both the Pentium D and the Athlon 64 X2 have 64-bit support, although again 64-bit performance is slightly better with the AMD chips.
Decent sources for benchmarks are:
http://techreport.com
http://anandtech.com
http://xbitlabs.com
. However, AMD's do tend to be cheaper and I hear they may have performance over Intels.
