The Asus' Intel Core i5-3210M CPU is notably better than the HP's AMD A83530MX CPU -
Link: http://novabench.com/cpuchart.php?a=1
However, the HP's graphics card is notably better than the Asus'.
Asus: http://www.videocardbenchmark.net/gpu.php?gpu=GeForce+GT+610
HP: http://www.videocardbenchmark.net/gpu.php?gpu=Radeon+HD+6620G
If you had to choose between these two, the decision would depend on what you wanted to use it for.
If it was me, I'd probably go with the Asus. The gaming performance of the HP would probably be a little better, but not much. At those resolutions, the CPU plays a big part.
If you want my advice, go on Amazon, there's a Toshiba laptop with the same CPU as the Asus, but a better graphics card. 6GB of fast DDR3 RAM - Not 8GB like the Asus, but 8GB is over-kill and the Toshiba's is faster. It can be bought directly from Amazon themselves in used but good condition for 374.09, or 429.99 new (still very cheap for what you're getting). It's at: http://goo.gl/QsXZP
There's a Samsung that's also a good buy. Same specs as the Toshiba except less HDD space. It's at http://goo.gl/FKeQ6
Pay no attention to G.Uk, Windows 8 hardware requirements are the same as Windows 7.
All the best,
Jason