The 777 wing was designed to be super efficient in cruise using latest wing technology and understanding.
The 747 winglet is there to increase span length without having to change gate size requirements. It is not as efficient as a blended winglet, but that is part of the "Not invented here" ego issues within Boeing. Aviation Partners has a blended winglet design that is 14 Ft tall and has been flight tested, but they were strangled by Boeing Senior Management when they started marketing it without permission.
Now the new 777-300ER has winglets, the raked kind. Harder to see unless your standing underneath the wing. They were designed a long time ago(I have 707 marketing photos with Raked wingtips
).
But..........one has to be careful when you grow an airplane many thousand pounds beyond its original intended design MAX weight. If you don't redesign certain things, winglets can cause you much headache and frustration.
