First a clarification. The phrase “right to work” is a misnomer that has little to do with the right of a person to seek and accept gainful employment. Anti-union proponents use “right to work” to refer to an option under federal labor law that allows workers employed by a unionized employer to receive the full benefits of a labor contract without paying for any of the cost to gain those benefits. In fact, no employee anywhere in the country has to join a union and no employer has to sign a labor agreement.
As Tom Geoghegan explains clearly in his new book, it isn't just that workers not paying union dues work under the same contract, but that non-union workers in a "right to work" shop receive the same services from the union, including legal representation.
In Europe, if you decide you aren't going to join the union at a site where there is a union-negotiated contract, your employer will probably give you the same benefits as the union members, for a variety of practical reasons, and no dues go to the union. But the union has no obligation to non-union workers whatsoever. On the other hand, they do have a financial incentive to be responsive to and actively serve the membership. It is hard to deny that the European system results in a stronger labor movement.
Of course, this is mostly an abstract argument. Switching to the European model isn't exactly on the table as a political option in 2015.