Both. I've seen similar and own something similar to the Asus you noted.
Both are great machines with good reviews. I would be guessing this is not only about the budget but the gaming results.
http://www.notebookcheck.net/NVIDIA-GeForce-GTX-960M.138006.0.html sees a lot of green so your gamer should be fine with laptops with that GPU.
As to the 12 to 16GB RAM, it's in that diminishing return zone. As in less than a per cent point effect.
For you the Asus may be the right move.
I'm looking at getting a new laptop but having a hard time deciding between these two and I haven't been able to find any comparison reviews between the Asus zenbook pro and the newest version of the xps 15 with the infinity display. If anyone had any experience with these and could offer a recommendation, that would be great.
The specs of the two are:
Dell xps 2015 - 6th gen i7-6700HQ, 512GB SSD, 16GB RAM, GTX 960M graphics
Asus Zenbook Pro - 4th gen i7 4720HQ, 1TB HDD +256GB SSD, 12GB RAM, GTX 960M graphics
Im writing from the UK and the Asus is roughly £350 cheaper than the Dell