Depends on the application.
From what I measured on my boxes, my Northwood 2.8C P4 is about 10-20% slower than my Newcastle 3400+ for CPU-intensive long tasks like encoding and compilation, which means they have exactly the same performance for the dollar given current prices.
However, if you move on to non-numberchrunching things like PHP, Python and CMUCL-compiled Lisp code the AMD64 begins to be twice as fast as the P4, and mysql benchmark said the AMD is 3 times as fast, but I think I want to verify that the benchmark didn't screw up before I take that at face value.
For games there's a few CPU shootouts for HL2 and Doom3 out.