I'd say go with AA, the card and the airline. As noted, awards to Asia and Europe on AA metal are discounted much of the year so your daughter can immediately fly off on a nice vacation for 40K. Also, for at least the next two years, AA will still give flight mileage based on distance and not spend, so she'll earn many more redeemable miles with AA than UA as it will take AA at least through 2017 to move to a revenue based program.
If she goes with UA, she'll get the initial mileage bonus for the credit card but will earn next to no redeemable miles if she flies on discounted fares when she buys flights. And UA only occasionally discounts awards to Asia and Europe while this is a standard off-season offering by AA.
Also, flying AA (with US) means she can use DCA instead of the worst airport in the USA, IAD. If not satisfied with AA over the two years she'll be flying them, she can always move over to UA and get a new credit card.