Both winglets and raked wingtips are quite complicated stuff which have both advantages and disadvantages.
To say that some plane is "good enough without" or "don't need them" is oversimplified. Every planemaker tries as hard as he can to make his planes as efficient as possible in everyday use.
First let us have a look at the winglets:
Few planes have "true winglets", but one of them is the 737NG. A winglet is vertical. It has a cambered profile with the camber pointing against the fuselage. And it is installed with a negative angle of attack.
The purpose is to intercept the wingtip vortex and transform energy from the vortex into forward "thrust" - much like a sail on a ship.
Since the shape of the vortex changes mostly depending on the wing angle of attack (AOA), then the winglets are optimized for an average AOA.
Since angle of attack is a product of weight, speed and altitude, then it can vary a lot from take-off to landing. When the plane is flown in a way, for which the winglet was not designed (too light/heavy, too fast/slow, too high/low), then the vortex will hit in front of or behind the winglet. And all you get is extra drag and weight of the winglets to haul along.
Since winglets do not generate lift, then they have little influence on the wing structure.
Then Raked wingtips:
Raked wingtips are wingtip extensions which are designed in order to minimize energy loss due to tip vortex. They generate lift as the rest of the wing, so the wing structure must be beefed up to accept the lift from the extra long moment arm, meaning heavier wing structure.
And now the mixture:
The 744/330/340s have neither true winglets nor raked wingtips. They are rather a compromise between the two.
Real winglets would not work very well on these planes simply because they are too fast. The air in the tip vortex is accelerated and would at a/c speed at M=0.82 - 0.85 hit the winglet at almost sonic speed and generate severe transonic drag, and all the advantage - and more than that - would be gone.
On a 737NG mostly traveling at M=0.75 - 0.78 that is not a problem, since the air will hit the winglets at no more than M=0.90 or so.
Therefore the 744/330/340 "winglets" first of all are swept heavily backwards in order to accept extreme transonic speed. At the same time they are angled approximately 45 degrees outwards, which means that they also work as small raked wingtips when they can't generate forward thrust. They do generate a little extra lift in addition to little forward thrust when AOA is favorable. And they do reduce the vortex energy loss a little.
Now the 777:
I think that it is natural that an extreme long range plane as the 722LR/773ER has raked wingtips rather than winglets.
First of all, really efficient winglets would limit the speed to 737 level.
Secondly, A 777 taking off for a long flight is almost twice as heavy as when it lands due to the fuel burn en route. That would mean that for utilizing the winglets it would either have to gradually slow down during the flight in order to maintain the optimal AOA, or it would have to constantly climb to ultimate altitudes where the engines would be less efficient.
And who decides your altitude these days? The PIC or ATC?
The 777 has a new wing design utilizing the newest materials to its maximum. That limits the extra structure weight penalty.
Raked wingtips at least work positively all way from take-off to landing.
A 737 on the other hand will mostly fly for considerably less hours at more constant weight and at rather constant altitude, and then true winglets may pay off. As long as you don't overspeed them.
And then 744/330/340: Well, the designers went for something in between. That was probably a very clever choice or compromise. They accept high speed. Extra wing structure weight is small. And they have both advantages of true winglets and raked wingtips, but to a much reduced degree. You can't get it all.
We can be sure that all designers have done all the homework they possibly could in their wind tunnels - and all the structure weight penalties - before they chose a specific configuration on their planes.
Always keep your number of landings equal to your number of take-offs