Although it should go without saying that buying a new processor, unless you are upgrading your existing system, also involves buying a chipset, and that the quality of that chipset should factor into your decision. It is easy to forget about the chipset when considering different processors: chipsets are not nearly as exciting as processors. But the chipset has a major effect on the overall price of the system, the quality of the system, and the upgrade paths available to the system.
If you end up purchasing an Intel processor, than you would also be purchasing an Intel chipset, most likely Intel's P43 or P45. There are quite a few other chipsets available that will support Core 2 Duos, but assuming that you're purchasing these processors for use in a primary use desktop, the P43 and P45 are by far the most relevant, unless you want Nvidia's SLI graphics in which case you need an Nvidia chipset.
Both of those Intel chipsets have been praised for offering good overclocking headroom, good drivers, and all the features that most users will ever need. The Achilles heel of the Intel chipsets, however, is the integrated graphics. As you've probably heard, Intel's integrated graphics are not good. Even if you don't play games or watch high-def video, they are poor enough that you may still run into a slow-down. If you aren't buying a discrete graphics card, the Nvidia chipsets then become preferable.
On the AMD side, you're probably looking at buying a chipset from the 780 or 790 series. These chipsets are known primarily for their excellent integrated graphics, as the take advantage of Radeon graphics cores. This makes them a much better choice for the avid user of multi-media, or a user who occasionally games. Considering that the chipsets from AMD do not have a higher average cost than the chipsets from Intel, and are in fact usually quite a bit cheaper, there seems little reason for anyone interested in a decent IGP to go with the Intel chipsets.
The biggest difference between Intel and AMD in this scenario is the one I've be tip-toeing around so far: the socket. AMD motherboards use AM2/AM2+/AM3, while Intel uses LGA775. The victor here is clearly AMD. It is hard to justify buying an LGA775 chipset when Core i7 has arrived and LGA775 is effectively without an upgrade path. AMD, meanwhile, offers a solid upgrade path for its users, as there is no major architecture change planned until 2011.