If you're running short on time, flying a carrier from a different country may reduce the time you have to sit in immigration. Yep.
Quite simply, most airlines tend to carry passengers who are citizens where the airline is based. Which also means, if you're a non-citizen, there will be less non-citizens on the flight, making your turn in line pretty short when you go through customs. It might not work for every airline (or country), but it's something that makes sense. Flyertalk user l'etoile explains it pretty well:
I generally find the majority of passengers on a carrier will hold citizenship in the country where the carrier is flagged. I find this useful as if I opt for a carrier flagged in a country I'm not a citizen of I am often only one of a few clearing immigration as a non-citizen, making my wait time rather short.
So now here's an obvious question: why didn't I think of this before?