The 777 had a wingspan length constraints of 200 ft. maximum (it ended up at 199'11"), which was probably based on airline input (presumably to fit 747 Classic gates). Some airlines also wanted folding wingtips to fit DC-10 gates, but no one ordered that option in the end.
Traditional thinking is that if you can get away with it, additional span is superior to a winglet. A winglet also adds structural complexity because it adds a bending moment. Then there is weight cost to consider. Boeing and Airbus will do exhaustive trade studies on things like this, and for the 777 the winglets did not earn their way on. But also remember that the early 90's computing technology was not what it was a decade later.
The 747-400 winglets do have a small cruise benefit, but it only shows up for mod and long haul flights (hence the 747 Domestic for Japan does not have winglets or the -400 wing extensions). These were designed empirically (with wind tunnel trials). Once influence for them making their way on the -400 was the looks - the airlines saw the mockups and liked them for their logos and distinction from the 747 Classic. The MD-11 winglets were no doubt influenced by the 747-400, were likely also empirically designed, looked cool, and were integrated into a tip extension design added to the DC-10 wing.
The 737 winglets are not "stupid" because they are large, and in fact some airlines like them for their distinctive look. They are the result of more advanced understanding of their function, as well as much-dvanced computational techniques (CFD). The promo materials for the Aviation Partners winglets also suggest a benefit for lower speed operations (takeoff, climb) which can be huge for noise abatement reasons. For an already-designed wing, the 737-ish design may make sense.
When you have a clean slate to work with, you might choose additional span as it is more structurally efficient. If you can meet the airplane performance criteria, why bother with complex and costly winglets. This probably holds for the A380. The 787 does not have winglets, but raked (swept back) wingtips like used on the 767-400. Again, there decisions were probably the result of trade-studies among the various options. As for Airbus, the 320 "winglets" look to be little more than tip fences that reduce the spanwise flow at the tip (one of the general winglet benefits), that also happen to add some level of distinction versus the older 737's.
There are probably some people out there (the Aviation Partners principals - at least some of whom are ex-Boeing) who think that all new airplanes should have a similar large winglet design instead of the raked wingtip. Who knows which is better, but if the AP was so great for a clean-sheet wing, Boeing probably would have included it. Airbus wouldn't be allowd to "use" the AP design because AP has some sort of agreement in place with Boeing.