In the long run the 380 will probably win but it could have problems in the short term. The 747 is such an old design that Boeing have recouped their design costs long ago and therefore will be in a position to severly undercut Airbus. (assumes both manufacturers are operating in a commercial way!)
The other main problem for the 380 is that its just so damn big. It does not fit into the present parking areas and terminal gates - the airport operators will need to spend big bucks to accomodate it. It will be fun to see the first time two 380's go tech and we have an extra 1000 pax sitting in the departure lounge.
As for Notso's comment on the damage to 777's - the 380 is an extra 20 meters wide (same length as 777-300) so expect to see more bumps on the ground in the future.