Skyrim is a game where you need to have both a good cpu and a good gpu.
The cards that you stated above both are good enough for skyrim. http://www.tomshardware.com/reviews/fx-8350-core-i7-377...
In this benchmark both setups use the same graphics card but you can sure see the significant difference.
If it's just for Skyrim, you could go a little cheaper. A GTX 660 or Radeon HD 7870 would be sufficient. The only exception is if you do very heavy texture modding, the extra memory on the HD 7950 may be advantageous.
I play with a GTX570 and I get frustrated. The load on the GPU only gets hit ~25-60%, but with lots of mods the ram usage just gets pegged. So it is not that you need a super high end GPU setup to play... but the more ram the better.
2GB minimum, preferably 3GB