I prefer the side sleeper over the standard hands down. With that said... I might have a gen 1 standard and a gen 2 side sleeper. I cannot attest to the current "standard model".
For me, the standard is much too thin and tends to slide out from under my head. Solution: wrap my puffy vest around it like tp with the tail of the vest on the bottom of the pillow and leaving a small tail. I can them pin the tail between my shoulder and the air mattress to hold it in place.
The side sleeper... according to me... is greatly improved but not perfect. The scalp feels more pronounced (good) but could be more so just a touch. There are little tabs with grommet holes on each side to run 1/8 or 1/16" shock cord. I cannot recall. I have done this and it holds the pillow securely in place. I have the shock cord relaxed but almost no slack in it. I run a 25" wide pad. This causes it to squeeze the pad and the pillow does not get away. Although the extra height is an improvement, I would love to see another 1/4" to 1/2" of height... but I do have wide shoulders. That is probably just me. I fixed this by tossing a beanie or piece of clothing between the pillow and pad and the shock cord hold everything in place.
Between the 2, unless you are a smaller framed back sleeper, I would say 95% chance you should get the side sleeper version!
Probably more of a write up than needed for a pillow but I hope it helps.