You’re meaning specifically the center hole? Both types of holes are functionally identical and can be used on the same types of shafts.
BrickLink (a useful and typically default Lego index and 3rd party marketplace) seems to only differentiate between these axle hole types as a footnote since they function identically. This piece is one of only a few instances I can think of where they do even mention it, and they call them x Shape and + Shape.
However, the wheels that you’re talking about are different beyond just the shape of the hole. The Sand Green wheel in 10317 has its center hole flush with the other holes on both sides. The mold variant in White has its center hole sticking out past the other 6 holes on one side; this is more clear if you click on 3D/Large Images and rotate the render around to see the opposite side. If you switch the wheels on the Defender, you’d probably be best off orienting the white wheels with the extended center hole sticking outward and then either removing the Light Bluish Gray axle spacers at the outside of each axle shaft or locating them at the very ends of the axle shafts.