ATI or NVidia GPU, AMD or Intel CPU?

I have recently started looking at parts for the computer I plan to build over the summer with my dad. We've already gotten a case that looks like something out of Tron (The movie.) and now we're arguing over AMD or Intel for the CPU and ATI or NVidia, for the GPU. We DO plan to install Fedora onto it once we're done. But my dad and I are not seeing eye-to-eye on the processor and GPU. I want to use ATI and AMD for the proccessor and Graphics, but my dad wants to use NVidia and Intel. This is really getting old so I said I would ask on a forum and the processor manufacturer and GPU Manufacturer that got a majority of good praises would be the Processor and Graphics card we would pick out. We already have most everything else picked out and checked to make sure that the two Motherboards we picked were compatible with our GPU's and CPU's we picked as well as the rest of the parts. My dad picked a Mobo compatible with the Intel CPU and NVidia card he chose, and I picked a board compatible with the AMD and ATI Card I chose. Now I ask you, should we use an AMD or Intel CPU and for Graphics should we use ATI or NVidia. Do note that in my experiences I've had better results with ATI Than NVidia. And also in my experiences my AMD Cpu on my lappy has ran cooler than any Intel CPU I've used. But my dad has had "better' experiences with Intel and NVidia.
So the CPU My dad picked was an Intel Core Sandy Bridge 8 core. I picked an AMD Phenom ii 8 core black edition. The GPU i picked was recently landed in the ATI Store and it was the Radeon 7880 with 6GB of Video Memory. My dad picked some Nvidia card, but I'm not sure what it was as he never told me and I don't use NVidia. And I also picked an ASUS Mobo and my Dad picked an Intel Mobo.

That's it. If you can help me and my dad decide which one we should use that'd be great. Majority rules here peeps. :cool: