Well I've had extensive experience with and without winglets on 747 all models and 737 200-NG. Although they undoubtedly give lower fuel burns, I have never felt any difference in handling qualities. It wasn't unusual for 747s to fly with only one winglet. Nobody would know unless they looked. Flying 737 300 (without) and NG (with), I noticed no handling difference. I guess I must have been a rather insensitive pilot! I always thought they made Boeings look fantastic and sleek.
Their benefit is cruise only, which is why really shorthaul operators don't invest in them. I've studied the Airbus 'sharklet' design and can only conclude myself that they are having a joke. The Airbus and Boeing designs don't resemble each other in the way that Tristars and DC10s resemble each other. They resemble each other like mirror images do! After that absurd little triangular plate Airbus used to stick on the end of 320-100 wings, we were told they weren't needed anymore, and now they come up with a superficially identical-to-Boeing winglet after all these years. Very peculiar.
I liked the documentary about the Boeing factory and the guy only known as 'the winglet guy'! Works on his own, nobody knew his name, doesn't talk to anybody- just comes in when needed, hammers the winglets into position with a large mallet, and goes away!