I found the EU server rejected my password (well, it wanted to send me an access code that never arrived), whereas the NA server logged me in without any problems.

I then went, logged onto the website which worked without any problems (showing that my password was fine) and changed the password. A few moments later I tried to log into the game again and that worked on the EU server as well as on the NA server.

For me, the problem is solved with that, but the above is a real security problem. It should never happen that a person can log in to one of the game servers but not to the other. In addition, I am noticing long waiting times (sometimes >1 min) to verify my user/password combo on the EU login server.