In general, Intel is a better choice than AMD because of performance. Intel CPUs can process more every clock cycle than AMD making Intel CPUs more efficient at running programs. An example would be a dual core Intel Core i3-2100 ($125) can beat a quad core AMD Phenom II X4 955 ($120) in all game benchmarks. However, the Phenom II X4 955 can beat the Core i3-2100 in many tasks that are multi-threaded like file compression and video encoding.
AMD CPUs are generally cheaper than Intel CPUs because of the performance difference. So building a computer around an AMD CPU is a little cheaper, but you do take a little hit in performance as well.
One thing in AMD's favor is that they are pretty consistent with their sockets types. They do not change socket types as often as Intel (which is about every two years based on a 6 year track record), therefore newer AMD CPUs are more likely to fit in a slightly dated motherboard than Intel CPUs. However, even though the socket remains the same, a new AMD CPU may require a new chipset to operate properly.