We tend to make a judgment call as we approach the border (as we're usually connecting to NCL) and if the EU queue is smaller than the other one we (I have a UK passport, and my gf and her daughter have US ones) will use the EU one. However, last Christmas the "Other Passports" line was a lot shorter so we used that, much to the annoyance of the passengers in the EU line. That said, one of the other passengers was going to have a much longer wait as he was using some very abusive language to the staff managing the queues and the immigration officer remarked that he wouldn't be catching his flight anytime soon