Some thoughts on why Europe has more problems integrating Muslims compared to North America
The 'militant secularism' of Europe is an interesting point which I haven't given much thought too. I think you're right that most European countries are more secular-minded and openly critical of religion than the US, or even Canada. This is probably an aggravating factor in terms of Europe's relationship with contemporary Islam. However, I suspect there are other factors that are more relevant than 'militant secularism'.
Europeans define themselves by their ethnicity/race to a much larger degree than North Americans. This also applies to their national identities too- they are defined by ethnicity, race, and language. The US and Canada consist of a much more heterogenous population, and most of the population conceptualizes themselves as being a descendent of immigrants (since most people can find an immigrant among the last few generations of ancestors). It only makes sense that Europeans would therefore be more prone to viewing newcomers with suspicion and sometimes hostility.
I think another factor is the emphasis on preserving history and the old culture in the continent. Overall, North American society is simply more dynamic and adaptable. North Americans are more willing, and capable, of altering their culture in response to changes in their demographics and changes in technology. Since their culture is more fluid to begin with, North Americans are less likely to become apoplectic about immigrants having some influence on the character of the society they live in.
I think another cause behind the differences between NA and Europe is that the fight for the rights of, and inclusion of, various minorities has generally been more successful in NA- at least in recent history. As a result of these victories for a more inclusive society, the sensitivity of North Americans to racial/ethnic/religious minority issues is more acute. To put it in a less flattering way, North Americans are more likely to have 'Politically Correct' views; and to use my friends terminology- North Americans are more 'militant' when it comes to the toleration/acceptance of minorities.
Europe of course has a very different history. I think it is no exaggeration to say that the majority of largescale racial and ethnic conflicts in Europe in the 20th century have either led to the disintegration of multiethnic nation-states, or worse, the elimination of the minority prescence. In the US and Canada, most major racial, ethnic, or religious conflicts have been successfully addressed without resorting to the fragmentation of the state, or wide-spread massacre (the major exception being the Native population- however, the worst of that abuse occurred several generations ago). I believe these different historical backgrounds have produced very different cultures. In NA there are strong cultural norms and attitudes that decrease the likelihood of conflict between diverse groups (some examples: American historical 'amnesia'; downplaying of ethnic roots; optimism; an orientation towards the future rather than the past). Of course the emergence of the EU goes against the generalizations I've just made about Europe. I think the EU might have a very positive transformative effect on old Euro culture- particularly with the inclusion of Eastern Europe and possibly Turkey. The shock therapy of integration might breath some life into a somewhat fossilized culture.
Finally, I think Europeans are just less libertarian in their outlook. They're more likely to expect individuals to adapt to the community, and correspondingly less inclined to have a live and let live attitude. This inevitably leads to more hostility towards Muslims, or any other immigrants, who actively resists adopting the cultural norms of the native inhabitants. And yes- one of the most important cultural conflicts is the clash between the 'militant secularism' of most Europeans and the non-secular attitudes of many Muslims.
P.S. Yes this post is filled to the brim with sweeping generalizations. There are definitely large differences between the various nationalities of Europe. But most of what I said was pretty general and I do think the comparisons hold for most European countries. Of course, it should also be noted that there is a huge amount of individual variation and I'm only talking about the 'average' European and North American. Anyways, I'd appreciate to hear any comments, especially from any Euros out there- or better yet people who have some knowledge of both continents.