I don't have any proof, but I suspect the best choice could vary with the player's hand physiology. What is best for the student?
I don't really buy into the 4th finger is weak and needs help from 3. Just did an experiment. With 1,2,4 the biggest stretch feels like it is between 1 and 2. With 1,3,4, the biggest stretch feels like it is between 3 and 4, The angle of my hand/wrist rotates a bit to cover the stretch. I have always used 1,2,4 on upright, and 1,3,4 does not feel any weaker or stressful on my hand. In fact it felt strong and comfortable.
If I try to wiggle my fingers independently, it seems different motions activate different interlinkages. Overall the strongest and most common interlinkages seems to be between 2 and 3; suggesting potential merit for 1,3,4.
The scale of the instrument is also a factor. I use something resembling one finger per fret on bass guitar. My observation is I use 1,2,3 much more than 1,2,3,4. Also 2,3,4 seems noticeably weaker than 1,2,3. So 2,3,4 is my least preferred option. In order to cover the reach with 2,3,4, it seems like I have to spread my fingers as if I am playing 1,2,3,4. There are times when I revert to 1,2,4 on bass guitar. Given the scale of bass guitar, covering a half step with 1 to 3 seems too cramped.
These are my observations in regards to how my fingering hand seems to work on my instruments. YMMV.