It depends very much on a situation.
If some characters are falling to a chasm then I don't think the size has any effect on damage.
However, falling from a large tree is different for humans and haflings, for example. For me at least. For the record, halflings are small
Consider a situation when a grown man is falling from the tree and a child. My money is ...
A couple of edge cases spring to mind:
Picture two creatures hanging from the ceiling of a tall room. If one is 10 ft taller than the other, it has 10 ft less to fall before hitting the ground. Therefore, taking the creatures size into account it would take 1d6 less damage.
Dimension Door mishap damage
If you would arrive in a place already ...
I could find no such feature; here are the best I could find
The Githzerai Anarch has a Lair Action to move an object and the DC changes based on the object's size:
The anarch can magically move an object it can see within 150 feet of it by making a Wisdom check with advantage. The DC depends on the object's size: DC 5 for Tiny, DC 10 for Small, DC 15 for ...