He plays games (naturally) should it be an ASUS G46VW-BSI5N06 Intel Core i5 3230M(2.60GHz) 8GB Memory 750GB HDD 14.0" Notebook Windows 8 64-Bit or HP E0M72UA Intel Core i5 3230M(2.60GHz) 4GB Memory 750GB HDD 15.6" Notebook Windows 8
Asus is the better brand. Those processors are the same. 8GB memory is better. Hard drive doesn't really matter.
Really what you want to look for here is the best graphics possible. If you can get higher than the Intel Graphics 4000 that comes on those it would be ideal. Depending on your budget you might even be able to get something with a discrete graphic card -- that would be better.
You should get a laptop with a dedicated graphics card, it's a world of difference in games. Even if you have to trade off an i5 for an i3 you should get dedicated graphics, playing games on intel is not a good experience.
Edit:I looked at the specs and it seems the Asus you posted has dedicated graphics, you should go with that one.