Of course it'd have no problem running on ultra at that resolution since he also has that i7, but AMD would be the better choice if he one day has $150 or so for a better monitor
The 7870 XT beats out both of those cards in regards to price/performance too, even if it runs as hot as a GTX 200 series card
At higher resolutions AMD wins out for BF4
http://www.bf4blog.com/battlefield-4-retail-gpu-cpu-benchmarks/