The two aircraft don't really define the way things are going in the aerospace industry when you consider that: -
Airbus had to build the A380 to allow it to compete with Boeing across the entire product range. If it hadn't then Boeing could have launched derivatives of the B747, this is harder to do against a new product in that area.
Boeing had to build the B787 because its B757/B767 are old and getting very few orders when compared to the newer Airbus A330's etc so it is in their interest to develop this area further rather than competing directly with the A380.
I believe that there will be a place for both aircraft types in the future market. The last few times I've flown into LHR I've been delayed circling over London for 30 minutes or so. More larger aircraft would mean fewer delays at these hubs which are mnot going to disappear. Additionally some airlines will develop some of their routes from regional airports and therefore need mid-sized aircraft.