When we treat the War on Terror like the War on Drugs or the War on Poverty, then we accept the impossibility of winning. Instead we adapt to a European mindset of managing the fallout from the latest batch of attacks.
There are two models for fighting terrorism. We can see the terrorists as an external invading force that has to be destroyed or as an internal element in our society to be managed.
In the War on Terror, Bush saw terrorists as an external force that had to be fought while Obama sees them as an internal element to be managed. And while both men signed off on some of the same tactics, their view of the conflict at the big picture level was fundamentally different.