Currently I'm using a reference design GTX 660. It's way better than the inn03d iChill as I had before. It has even higher clocks at boost 1110,5 vs. 1084,5, and it is way cooler 72*C at max vs 85*C.
You might consider getting Radeon 7870 because it's 5-7% ahead in performance at stock speeds, nothing noticeable. Though it uses a bit more power and is a little noisier, if you compare reference cards, but it's also a little cooler.
Cooling on the two different chips has different thermal limits, so you can't really compare the heat, because some cards are meant to be hot, and doesn't get much affected by it, while others do.
In the end, what brand you favors the most will be the optional choice. If you like the drivers and the cool technologies from Nvidia that would be your choice. If you like raw power and good overclocking capabilities, go for Radeon 7870.