Registration of a European Trademark

The short and simple answer is "probably not" if the Netherlands company has registered their mark thoughout the EU but possibly if it has not registered its mark in the EU. You also maintain the option to register the mark in specific EU countries where your services are marketed that do not overlap with the Netherlands and possibly Belgium and Luxembourg as well (since they have a treaty unifying their trademark system).
As with any legal question, the answer depends upon many specific facts and exceptions typically abound. For instance, if the Netherlands company wants to do business in the U.S. and register its mark here but your U.S. registration and use blocks the Netherland company's use/registration of the mark in the U.S., you might be able to negotiate an arrangement with the Netherlands company to allow your marks to coexist on both continents. Therefore, it is strongly recommended that you consult with an attorney. In this case, probably a U.S. trademark attorney should be consulted first because most trademark attorneys maintain a network of trademark attorneys around the world and the consulted U.S. attorney probably knows a European trademark attorney to consult.