The operating and incidental costs of owning a graphics card are trivial. It's futile trying to spin them as important unless you have hard numbers. Given the cost of electricity you shouldn't be worrying about that unless you're on welfare.

With respect to transistor density nVidia and AMD count and use their transistors differently. One reason for the density difference could simply be physical constraints - running shaders at 1600Mhz isn't free. The scheduling and scoreboarding logic on nVidia chips is also much more complex and may not be high-density friendly. There's also been talk of AMD simply being better at semi-conductor design. In the end none of that matters to an end user of the product though.