Different scheme are almost universally recommended for tire rotation on front drive and rear drive cars. See, for example, these instructions by people who should know. The general idea seems to be to keep the tires coming from the powered axle on their respective sides and swap the sides of the tires coming from the unpowered axle. Curiously, the rationale is never given.
I imagine that in practice the difference between the two ways is marginal, the important thing being that each tire ends up at each position. However, I’m still interested to know the rationale for using a different scheme based on whether the car is front or rear drive.