The answer to this question certainly depends on the system configuration. On average, an Intel motherboard will require more power than an AMD board, as the chipset includes the memory controller, which AMD integrated into its processors. This happened for performance reasons, but the side effect clearly is better efficiency. However, the differences in voltage regulator layout and high-end vs. budget chipsets on a motherboard can also negate my statement - especially as you go into the high-end, where motherboards are filled with additional components.
If we assume that all other components can be used for either platform, differences can only be found on the processor and motherboard side. The power supply, RAM, the hard drive, and the graphics card are standard components for both AMD and Intel systems.
The question now is: how will the power consumption be if we assume certain usage scenarios? It is not difficult to predict this for systems that run idle or when they're at full load, but this does not reflect typical PC usage. Instead, we decided to use SYSmark 2007 Preview to simulate typical user behavior, and looped runs of 3DMark06 and PCMark05 to stress the system a bit more.
We didn't select high-end processors, because Intel's Core 2 Extreme would leave the AMD Athlon 64 X2 family in the dust. We decided to use reasonable mainstream processors that are known to be somewhat energy efficient: an Athlon 64 X2 5000+ using the firm's 65 nm manufacturing process, and an Intel Core 2 Duo E6400.