The short answer: Whichever airline offers a nonstop flight to my destination. Since my home airport is EWR, the almost always means United, where I have status.
In general, I much prefer the legacy carriers and will choose them over Southwest even for a slightly higher price. I greatly value the miles I accrue and spend them for international vacations with my wife. The inability to travel to most foreign destinations with airlines like Southwest and JetBlue make them pretty much a waste to me, unless the price is really right.
Reading the comments, I'm surprised how few posters seem to care about international award travel. Do folks here just spend most of their vacation time at Disney? Do they not fly enough to accrue enough miles to redeem?