I haven't seen this thread surprisingly. Which of the brands has a lower power consumption, overall performance, better graphics, price, quality, reliability, satisfaction, etc. Pick the overall winner.
Brand power consumption clearly is lower for AMD. Less letters in the logo make for more power efficient branding.
Brand performance is clearly better for Intel, look at all those corporate contracts.
Brand graphics is a tie for me. Both the AMD and Intel Logos aren't anything special
Brand price - well, AMD is definitely the cheaper brand to buy, but that's because it has less value. I wouldn't buy the AMD brand at the moment, and I don't think anyone can afford to buy the Intel brand.
Brand quality is again dominated by Intel. They marketed even the anti-trust issues away.
Brand reliability - mixed bag. Intel messed up with bad press for the Pentium 4, AMD had the non-throttling K8s (or were those K7s?) that burned away, and recently had the Bulldozer launch which ruined the old FX-sub-brand.
Brand satisfaction - I think both brands have satisfactorily helped sell the products of each of the companies. With the extension of the AMD brand to GPUs, they have clearly deemed that brand more satisfying than the ATI brand.
The overall winner is Apple, because even though they sell Intel chips, none of their massive customer base really cares about it.
I hope this brand analysis was helpful!