Other than the recent clown the US has elected, does the EU really feel like a "vassal"? Do people toil against their will, yield their culture to another power? In Australia we're even more so a "vassal" of England, but we're as Aussie as Aussie can be. Life wouldn't change a zack if we separated from the UK...we'd just be a Republic I suppose?
I can't imagine the EU should feel particularly different? (other than Ukraine and the recent shemozzle)