It depends on processor generation,
486 and Prior, AMD had the cheaper chip, and since technology was essentially non-existant (compared to today, there was no MMX, SSE, 3DNOW etc.) there was no reason NOT to go with AMD other than popularity.
"Pentium" Era, AMD still had cheaper chips, and it wasn't until the Pentium MMX came out that AMD started to look bad, but given all of the problems the Pentium had with flop/div i'd say AMD was still the better choice.
"Pentium II" Era, Intel innovated here, they had the faster processors with the better technology. AMD had 3DNow, but that didn't really matter all that much...
"Pentium III" Era, I'd call it a draw, Intel and AMD had comprable processors (i guess a slight performance edge to intel), and only price gave AMD the edge, and even so, the price differnce wasn't all that much.
"Pentium 4" Era, AMD, totally AMD, First consumer 64 bit support (even if it's not useful, or complete), better quality, Hypertransport, and lower price totally blocked out that whole HyperThreading bullshit (and it was some plain old bullshit)
Dual Core Era, Intel. Despite Intel's dual core processor being two cores on one die (where as AMD has two totally independent cores) intel beat AMD to the market by at least 6 months.
Quad Core Era (ie: now), Intel. one word: Phenom (totally sucks shit...)
Of course, that doesn't take into account mobile, server and budget machines, places i think AMD does well in most of the time.
As much as i love AMD for being cheap, and the honest to goodness better processor (any AMD with the same clock speed as a same generation Intel will beat it hands down), they have failed recently due to their inability to put out a product that is quality.
AMD needs to start putting more cache memory on their chips, they have always had less than their intel's counterpart, but when the rival's top end in rocking 12mb L2, and you're rocking 2mb L2 (and a 2mb L3) then there's a problem here.
When the next generation comes (that would be the 6/12 core generation) we'll (hopefully) see a tie again, from what i can tell both Intel and AMD have a 6 core processor roadmapped within 1 month of the other, both look great on paper, but until real world performance is benchmarked it's impossible to call a winner.
So in short:
Single Core: AMD
Dual Core: Intel
Quad Core: Intel
While AMD may be cheaper, performance is key, i'd rather pay more for a workhorse. (unless i'm looking for a cheap computer)