Hello,
In fact the waltz of the monsters is a waltz in 3/4
If you write it in 6/8 it becomes a march and not a waltz.
There is a very telling example:
The return of the swallows which is a waltz in 3/4 which is also played in 6/8, but this changes the piece completely.
Many accordionists finish this waltz in march.
Besides, you can play all waltzes in 6/8, but I don't see the point.
To conclude, writing in 3/4 means that it is a waltz while writing in 6/8 means that it is a march or a tarantella for example.
What is important is what a measure contains. In both examples the measures are not identical, so the interpretation is completely different.
Sincerely
NB: I'm looking for the return of the swallows with the two versions I've already seen on the net. If I get my hands on it again, I will post it.