The following article from Xbitlabs.com is a bit dated (August 2006), but it does compare the Core 2 Duo E6300 and three Athlon X2 64 CPUs with TDPs of 35w, 65w and 85w.
AMD’s Response to Intel Conroe: Energy Efficient Athlon 64 X2 CPU
It's not really a direct comparision of compariable CPUs because the article compares the X2 3800+ (35w), X2 4600+ (65w) and X2 4600+ (85w) CPUs verses the E6300. The E6300 direct competitor would be the X2 4200+/4400+. However, the article isn't about benchmarks, it's about power consumption so the article should give you a general indication of how the various Athlon TDP CPU stacks up against the E6300.
In a nutshell, if the CPUs were simply idling, then Athlon CPUs will consume less power than the C2D E6300 CPU:
http://www.xbitlabs.com/articles/cpu/display/amd-energy-efficient_6.html
However, the picture changes a little bit when 3DMark06 is used to stress the CPUs. As can be seen only the Athlon 3800+ (35w) consumes less power than the E6300 by 20w. But the X2 3800+ is also a slower CPU.
http://www.xbitlabs.com/articles/cpu/display/amd-energy-efficient_7.html
The difference between the E6300 and the X2 4600+ (65w) is 15w. Generally speaking it is not surprising that the X2 4600+ consumes more power because it is faster than the E6300. If an Athlon X2 4200+ (65w) or 4400+ (65w) were compared, then the wattage difference will be less.
In my opinion, if you can find a 35w TDP version of the Athlon 64 X2 5000+, then it may (or may not) consume less power than a comparable Core 2 Duo CPU. However, the 65w TDP version will almost definitely consume more power than a C2D CPU.
If power consumption is really your main concern then you need to take a look at the video card you are using as well as the power supply. In general, ATI video cards uses more power than a comparable nVidia card. The only exception at the moment is nVidia's DX10 8800GTX GPU. This card consumes more power than any single ATI Radeon GPU, then again ATI does not have a comparable DX10 vidoe card for sale at the moment.
The following are a few power consumption articles from Xbitlabs.com:
Faster, Quieter, Lower: Power Consumption and Noise Level of Contemporary Graphics Cards
ATI Radeon X1950 Pro against Nvidia GeForce 7900 GS (page 6)
Directly Unified: Nvidia GeForce 8800 Architecture Review (page 11)
ATI Radeon X1650 XT Graphics Card Review (page 4)
In every case, the nVidia GPUs consume less power than their direct ATI GPU competitors. For example, the Radeon X1900XTX consumes 120.7w at stock speed compared to 84.2w that the GeForce 7900GTX consumes. Of course, overclocked GPUs will consume more power than the stock speed versions.
The power supply unit (PSU) plays the most significant role in overall power consumption. It is always a good idea to set aside a decent amount of money for a PSU from $70 - $200 depending on how much power you are looking for. The reason why the PSU is important is because it converts AC electricity to DC electricity. This conversion is not 100% efficient, there is always a power loss when converting one to another. The electricity that is lost is converted to heat.
The peak efficiency of PSUs ranges from 65% to 85%. Low cost PSUs (read as cheap) are generally on the lower end of the scale while more expensive PSU tends to be more power efficient. My general preference is just about any PSU made by Seasonic. That includes thier own namebrand, Corsair, and the Antec NeoHE series. Seasonic PSUs tends to be very efficient, very quiet, and very reliable. They also tend to be more expensive than your average PSU.
The Seasonic S12 Energy Plus SS series is one of the most efficient PSU you can buy. They are rated up to 88% efficient. Here's an example:
SeaSonic S12 Energy Plus SS-550HT ATX12V / EPS12V 550W Power Supply
So how does efficiency affect your total power consumption? Assume your gaming PC consumes 300w of power when you are playing games. 300w of power is the average powerful gaming PC with a high end CPU and a single high end GPU. PSU #1 is 70% efficient, PSU #2 is 85% efficient. The following is the amount of power the PSU will draw from the AC outlet from a simplic point of view:
PSU #1
300w / 70% = 428.6w
PSU #2
300w / 85% = 352.9w
As can be seen above, the PSU alone can mean difference of 75w of power consumed.
However, it is a bit more complicated than that. You want to match up the "right size" PSU to the amount of power your PC will be using. The load placed on the PSU also affects the efficinency. Assume the following characteristics for two 85% efficient PSUs, PSU #1 is 450w and PSU #2 is 1000w.
Load %....................................Efficiency %
1 - 30..........................................50
31 - 45........................................60
46 - 65........................................70
66 - 80........................................80
81 - 95........................................85
96 - 100......................................80
PSU #1 (450w)
Load = 300w/450w = 66.67%
Efficiency = 80%
Power drawn from AC outlet = 300w/80% = 375w
PSU #1 (1000w)
Load = 300w/1000w = 30%
Efficiency = 50%
Power drawn from AC outlet = 300w/50% = 600w
The above examples shows that even though both PSUs are rated up to 85% efficiency, PSU #1 (450w) will waste less power. The moral of the story, don't buy an excessively powerful PSU unless you know you will tap into that power later on.