Originally Posted by
notquiteaff
There is no formal exit passport control where you show a passport to US authorities. The airlines ask for passport information during Online Checkin and may additionally want to see the hard copy at the airport. As far as I know, they use that information to determine whether a visa requirements for the destination are met. I assume they also pass that information to US authorities to enable them to track who has left the country. If you enter an EU passport into the airline system when departing for the EU, that would be a mismatch with the US passport you used to previously enter the country.
There are formal exit controls everyday on some flights. CBP targets flights at various airports around the US daily. As I, and others have noted, this is common enough, though not likely to affect someone flying less targeted routes. Normally CBP is searching for FinCEN type violations but immigration is targeted and often times by full computer passport swipes. That said, even if a flight is targeted for full enforcement you leave the US on your US passport and enter the EU on your EU passport. "mismatches" are not an issue as the airline manifest is not the primary tool. The actual passport presented to an officer is. Dual/multi citizenship is not a foreign concept (no pun intended) to immigration enforcement officials in North America or Europe. Some airlines, such as United, allow multiple passports to be saved in the profile for travel anyway.
I leave the US on a US passport and entire the EU on an EU passport at least ten times a year. It is a simple and painless procedure that some unwillingly try to over-complicate.