They don't get a choice usually, partly due to protections set in law and partly because there isn't enough labour competition for them to only pick non-unionized workers.

Also in countries with well established unions like Germany, the employers expect the union to be equally responsible for some [productivity guarantees in return. It's less of a one sided deal. I believe in the recent recession, many union workers there agreed to a lesser pay in return for the employer to retain the whole of them employed.