The 820m is not something that is gaming capable by our day and age.
I could overclock my old 540m and likely match it.
The CPU's are comparable, however when your gaming your typically GPU bound so I would go for the Asus unit
You could look at the m4600 or the m6600
They are still very adequate for today's requirements (unless you need a new instruction set or something)
For example with my current set up I get about 70-110 FPS in Deus Ex: Human Revolution at 1080p.
They are obviously heavy machines though, but relatively cheap.