I would think it's more dependent on the engine and what the manufacturer recommends - not necessarily gas or diesel. I also always warm an engine up before changing the oil so there's a good supply of oil everywhere. If I had an upside down filter and it was easy enough to pre-fill it, I would do it since it definitely can't hurt.Is this different for gas vs Diesel engines?
I let the filter finish draining into an old oil catch pan overnight. Then it goes into the regular trash. If there's a local option to drop it off somewhere, like oil, I'm not aware of it.