The WilderNest opens to the passenger side, which is my experience with a sort of RTT. In that case there was no choice.
I will say one reason to open towards the driver side is if you have to orient the truck in such a way that makes getting to it funky, say a ditch or hill, or you have to level the truck a lot so one side is a lot higher than the other you can position things such that the side that is up in the air isn't the one where you have to get in & out of the truck. Also opening and closing it on the side that's not 9 feet in the air is much easier.
But FWIW I was told the reason WilderNest chose the passenger is it's easier to use in established campgrounds. Not sure why that might be or even the validity of that. Could just be semi-drunken speculation on our part, too. But when you think about it RVs and travel trailers have their doors on the right side so I dunno, maybe there's a reason for that. State parks seem to orient things like picnic tables and fire rings so the right side is pointing toward them. Shrug.