Well, Its very difficult to compare them... [Ya, really :-( ]

AMD:
1) Price
2) Get more done per clock cycle (that is why slower chips can tie or outperform Intel chips)
3) 64-bit processing (on Athlon 64s only; not yet supported by Windows, but a 64-bit version is in the works, so in the future performance of these chips will increase)
4) On-chip memory controller (again, only Athlon 64s; this allows faster, more direct access to the system's RAM and increases performance in memory-latency intensive applications)
5) Generally easier to overclock (be carefull with ANY OCing, though)
So.. Who is the winner ?
Well I would say "AMD is a winner,but Intel is not a loser" :D
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So i'll just mention their Advantages .. and decision is left to you :-)
As far as benefits of AMD or Intel CPUs, here is a (basic) rundown:
Intel:
1) Brand name
2) Faster core speeds
3) Hyperthreading (most models) [tricks Windows into seeing "two" processors,improves performance some (5%-15%) in multi-tasking situations; on rare occasion can DECREASE performance slightly in some applications]
4)Newest chips support LGA 775 (new socket type) and the matching motherboards have PCI express (new add-on interface) and DDR2 memory
As far as benefits of AMD or Intel CPUs, here is a (basic) rundown:
Intel:
1) Brand name
2) Faster core speeds
3) Hyperthreading (most models) [tricks Windows into seeing "two" processors,improves performance some (5%-15%) in multi-tasking situations; on rare occasion can DECREASE performance slightly in some applications]
4)Newest chips support LGA 775 (new socket type) and the matching motherboards have PCI express (new add-on interface) and DDR2 memory

AMD:
1) Price
2) Get more done per clock cycle (that is why slower chips can tie or outperform Intel chips)
3) 64-bit processing (on Athlon 64s only; not yet supported by Windows, but a 64-bit version is in the works, so in the future performance of these chips will increase)
4) On-chip memory controller (again, only Athlon 64s; this allows faster, more direct access to the system's RAM and increases performance in memory-latency intensive applications)
5) Generally easier to overclock (be carefull with ANY OCing, though)
So.. Who is the winner ?
Well I would say "AMD is a winner,but Intel is not a loser" :D