Hum, I just realized that those polar storms would turn easily into the hexagon if they just lose power (or would be covered by another layer of material over it). Both are probably the same phenomenon. More strong in Jupiter, less in Saturn. Tornados would explain also why is a tall shape

The hexagon should gyrate slower (with less energy) than the jupiter storms. Neptune should have also the same process but is colder I'm not wrong, so maybe it has less energy and is not so easily visible.

Yep, here is the Neptune hexagon... same pattern, same process

https://slate.com/technology/2014/05/neptune-voyager-images-...