Just for the record, flying with Madame means trying both passport lines as I have a EU passport and she hasn't. We were on Aerolíneas Argentinas from/to EZE, i.e. arrival at 1600 and departure at 1915 (working days in both cases). The two lines were completely empty at both times - EU was fully automated and the machines worked much faster than those at LHR and AMS, and crossing the "others" line took Madame less than 3 minutes. I guess it's a matter of luck, but we were very pleased.