I'd personally go with the Asus.
It won the Tom's 2013 'Smart Buy' award (
link to review), and is certainly more favourably reviewd on pcmonitors. Here's an excerpt from the conclusion for the ASUS VG248QE (
full review here):
"If you are after a really responsive gaming monitor without any input lag or potentially distracting levels of inverse ghosting to worry about then this is really a key player at the moment. If you live in the United States then this monitor comes at a truly excellent price"