very, very little to choose between them John. Laptops direct only list our model as a 'refurb'
here but i'm pretty sure they are still available elsewhere.
Slightly different processors, the one you showed is a fraction quicker and uses a bit less power but in real world terms you probably wouldn't notice it. The Acer has a wider screen (true 16:9) but the Asus has a deeper one - only really an issue if she wants to watch HD movies.
the Acer probably has a better sound card but the Asus has (on paper anyway) a more powerful graphichs card (personally I prefer Nvidia graphics over ATI as they have always been better at updating drivers and ensuring backwards compatibility
The Acer has a fingerprint recognition system for security and the facility to plug in an external SATA drive but lacks a firewire port (addon cards cost about a tenner) both have 4 USB ports
Laptops are ultimately down to personal choice, if she's going to be carrying it around a lot, then both of these are quite large machines and will need a decent case.
When we bought the Acer (it cost us £599 earlier this year), there was nothing we saw in that bracket which came near in terms of features. It looks great as well, the screen display is impressive for when I take it out to show clients stuff.
If we were buying today, I'd seriously consider the Asus you linked to but I would probably still buy the Acer considering it's now reduced price
Both makes have a decent name for reliability (at this end of their ranges anyway) despite there being some badge snobbery over the Asus brand.