My answer is "it depends". If we're talking adding 6 hours to an international itinerary by choosing a legacy carrier I'd be inclined to do a non-stop on a budget airline.
But generally, if it isn't too much more inconvenient relatively speaking, I'd take the legacy even if it meant connecting somewhere. I don't have much faith in Ryanair or Spirit types of ultra-LCC operations and I'd only pick them if there was a vast price difference between them and their competitors. Other budget airlines like Southwest I think I'd be a little more receptive to.