It's an uneasy cohabitation. The EU did not have great success in trying to deal with the former Yugoslavia's crisis. NATO had to go in and do the job.
The idea of trying to duplicate NATO's functions in Europe strikes me as a needless and wasteful effort on the part of the Europeans. It probably can be made to work, but to my mind it's not worth the effort. NATO functions, and it functions well. It is a good thing. It needs fixing in some areas, particularly in the areas that concern us, frankly. I was involved in a study that came out a month ago on what needs to be done to fix NATO. I think there are things that can be done to make it work better, but the idea of duplicating it by creating a European Union security force strikes me as a waste of time and effort.