Yes, they closely cooperate. But EU agencies (except for UK) don't have a record of torture, abduction and overly use of secrecy. Comparing the budgets of the various secret services should be informative. US agencies are WAY bigger and I think much too big. UK is the exception - being in line with US.
Well that's a facile statement, since the EU is only 20 years old. Individual countries in Europe absolutely do have a record of torture, abduction, and secrecy in varying degrees. Are you completely forgetting the 20th century?