That's a very interesting point. I don't have an answer to that, but I would point out that muslims in my own country, (Ireland), are also very well integrated even though we do have a welfare state, free health care, etc.
I think you've raised a very interesting point there, though. How much does welfare dependency feed into extremism, and why?
Oh i am sure there are exceptions to the rule. But i am talking generally not specifics.
The welfare system is the trap for not only Muslims but immigrants in general imo.
Infact i think welfare breeds only dependency on the state and is something that prevents people from working for their lifes not tto mention stops integration. There are people who are living off the state for generations in some parts of UK and what this does is breed a generation of those who take for granted what they have in UK.
The Muslims coming into US in comparison come from (generally speaking) well educated countries or are rather ambitious. The whole 'american dream'. Anyone immigrating to US knows it is no easy ride and are by default forced to accept the culture or society they have come into.
I'd like to say the foundation of US also plays a role. In US, no one is native (apart from the NA). It is a country of immigrants together so you can fuse yourself in easier than in Europe where you always will be the outsider in another persons country.
Not to mention this cock and bull ideal liberalism UK and Europe has where we tolerate intolerance