Thats a no brainer. ASUS is the best of two. If you could pick the older GTX460M graphics in the older generation of the same laptop it would be even better, because the 1.5GB 460M is marginally better than 2GB 560M which is actually a 'lower' model of the original 1.5GB 560M which you find in ASUS G74s. It has more RAM, but performance-wise it is ~15% lower due to low bandwidth.
2GB 560M = 128 bit - 40 GT/s bandwidth
1.5GB 560M = 192 bit - 60 GT/s bandwidth
In anycase the AMD 6770M is comparable to Nvidia 550/555M and almost 40% slower than 560M.
Good luck with your new laptop!
Awesome, thanks! It was the answer I was looking for as I couldn't find much info on the gimped 560m. And is the 6770M 40% slower than the 560M 128 bit or the better 1.5gb 560m 192 bit version?