Ok do not get A64 3400+. This means Socket 754.
P4 820 will be faster in all multitasking scenarios. For gaming, A64 will win, but this is largely dependent on how good your videocard is.
I would consider P4 920 over P4 820 however (there is a thread on this forum of how a user got 4.4ghz overclock from 2.8ghz.) This even beats with FX60 at 2.9ghz. I strongly encourage overclocking since it is very easy. For single core, you can get Opteron 144, 146 if you are on a budget.
If you insist on stock speeds, go with Socket 939 and A64 3200+. Of course digging deeper, surfing will depend on your Internet service provider, office work will be faster on P4 dual core vs. single core A64 in heavy multitasking scenarios (but slower when working with few programs since A64 has lower latency and will open individuals programs faster), and A64 will pull away in gaming scenarios. But if you have a weak videocard, the processor wont make any difference.