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.
The differences express themselves in such things as detaining terrorists at Guantanamo Bay or backing Islamist democracy. If Muslim terrorists are an alien force, then detaining them without trial is no more of a problem than detaining Nazi saboteurs was during WW2. And if Islamic terrorism is driven by alien impulses, then it has nothing in common with us and attempting to accommodate it cannot succeed.
Obama and the Europeans see Islamic terrorism as a social problem whose root causes need to be resolved rather than defeated. It’s the old model used for the radical left which was “fought” by mainstream parties adopting elements of its program to compete with it… with disastrous results.