Legal representation is probably the main exception. Other benefits you could just pay on your own, but unions are the easiest way to get access to lawyers specialized in labor issues, and they will often represent you for free.
The bigger difference between American and European unions is that Europe tends to treat union membership as sensitive personal information. Your employer has no legitimate reason to know whether you are a union member, and it's not allowed to ask. The union is also generally not allowed to tell its members which of their colleagues are members. Many of the issues surrounding American unions just disappear when union membership has no impact on your daily job.