ISO 400 on the 7D and 5D3 are completely different sensetivity levels and it's misleading to directly compare them.
Cameras are a function of geometry.
People have been misled with crop to full frame conversions for years.
The 5D3 was my first FF camera body. I previously used crops... 20D and 40D. As stated, I am evaluating either a 7D or 5D2 as a backup to the 5D3.
I am not a physics major and thus, I am not going to dispute Radiating's calculations and references to physics. I understand that it isn't a 1:1 comparison, but...
What I do know is that a photon of light is still the same size regardless of sensor and that a crop sensor 'extrapolates' the equivalent pixel dimensions due to the fact that pixel density is so great and thus pixel size is so small, that is is practically splitting a single photon of light.
I also know that at the end of the day, if any of us were to print either OOC image to their largest extent @ 300 dpi, that we would see the difference between the 7D and the 5D3 as seen clearly by these 100% crops and therefore, the reality is that a crop body's sensor is simply inferior.
Desiring to hold on to the 'reach' (cringe) benefits of APS-C, I wanted very much to keep the 7D as an all-around versatile camera and as a backup to the 5D3. After the pictures I took today, and the grain I see in them even at 50% (heck, even looking at the entire image sized to fit on a 15" laptop display) there is clearly an improvement in IQ from a FF body.
After evaluating the 7D, it's clear an APS-C is inferior. It's just the reality of physics. We can't shrink light any further, but we are trying to over-resolve it. Here come the arrows and darts...