I learned same side
three advantages:
torso rotation is encouraged (as discussed above)
TR is huge for power and endurance.
It’s easier for my body memory to push on the same side foot while pushing on the same side hand. It seems to help the hand work. Almost like a smooth shove, hand slightly lower than shoulder height. A little extra power at full extension,but the hand stays relaxed and never clenches, setting up for spin and transfer to other side.
By engaging each foot/hand on the same side a nice rhythm develops for me, and my thighs and calves are getting a nice regulated stretch. Keeps numbness away.