Airbus A380 first flight 27-4-2005
Boeing 787 first flight 15-12-2009
Not really the correct comparison.
I think the B787 will eventually be a game-changer but it might take another year or so to settle down. Boeing may yet lead the market with this product.
Airbus introduced an innovative VLA product to market with the A380 that Boeing didn't, but it also had numerous teething troubles. Despite Emirates best efforts the A380 isn't exactly a run-away sales success. However, Boeing's 747-8 has been a real sales disappointment so I suppose you could argue Airbus leads this segment of the market.
As for the B777 in it's various forms, surely Boeing must be regarded as a class winner to produce such a fine product in great numbers. I'm really looking forward to seeing what Boeing do to replace the B777.
Airbus does well with the A330 though, sitting below the B777 size aircraft and gets a tick in the box for it.
For me, the A320 v B737 debate is a waste of breath as they sell in roughly the same numbers and have attributes that appeal to different customers. I'd give them both a tick in the box for their respective products.
In short, I don't think either Airbus or Boeing leads one over the other overall. As each brings in a new model, you could argue they gain a lead but it a fluid game where each competitor leads the other from time to time.