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.

Hi, it is not clearly determined that you would like to register in which european country. Community trademark is not the only way of registration. you can file your trademark in other countries as directly national filing or via Madrid System. If your market is in Netherlands it is difficult for you then. Also, you have to check the situation of the Netherlands' trademark either it is a well-known trademark in one of EU countries. It seems like you need help from a European trademark attorney.

Hi.
As Alaxander and Yucel mentioned it depends on the country you are operating in, since trademarks cover a certain jurisdiction (country or region, e.g. the EU). On the other hand, the use of the company name of the Dutch firm gives them a certain right of protection that is comparable to a trademark, so they could oppose your registration for the EU. However, to do so their name has to have more than mere local significance. Moreover, if your main market is not the Netherlands, then you should also consider operating without a trademark.
Of course, this is not a full legal advise, but should give you an idea of options.

Yes, as Yucel wrote below you might need a European Trademark Attorney.
Also keep in mind that you may also register it in Switzerland which is a non-Eu member