To: Mutt
The B777 was a victim of the NIH syndrome (Not invented here). At the time of its conception, winglets were common on Airbus aircraft. Boeing didnt want to be seen to be using Airbus ideas so they spent more time developing the wing without winglets.
Airbus Industrie did not design the small winglets used on the A-310 and the A-320. Boeing designed them under a NASA contract. When the design was completed it was given (free) to Airbus but if Boeing wanted to use the design on their own aircraft they would have to pay a large licensing fee to cover the design costs. They opted not to use them and save a few bucks.