For one he has a right budget. The goal here is to build an excellent foundation for upgrade later so the computer as a whole will last longer. Replacing the CPU is a lot less expensive than buying a new computer. Also, the Z87 chipset is a faster chipset regardless of over clocking.
As for the comparison, it is actually pretty accurate. You realize the only real difference in the two's performance will be in numbers right? You won't be able to detect a real difference. Some games program towards AMD, others to Nvidia.
That CPU cooler is not good. It will not cool as well as an air cooler even.
These are VERY mismatched.
Get 8gb RAM minimum for this kind of build.
1300w is VERY overkill and will need to be replaced in a few years when you add a third card anyway. Get a 750-850w unit for 2 cards, then many years away when you add a third, get a 1000w max.
If you want to use more than 2 gpu's you will need the i7 not the i5. BUT, 2 gtx770s will be more than enough to max any game for a LONG time. 3 cards would be VERY pointless.