direction of turn
Assuming the radius of turn is the same in both directions, we teach that the handling pilot should be on the outside of the turn. Once you've commited to the turn, visibility isn't of much value. You're going for max deflection of the tiller in either case.
The reasoning is that you've got a better feel of just where you are relative to the edge of the pavement if it's on your side.
A good drill when you're new to an airplane is to put your flight kit on the ground outside your side window, in line with the outside edge of the main gear tire. Then climb up into the cockpit and look at where your kit is. In most cases, it will be much closer than you'd imagine it would be. In many cases, you can't see it. That means if you can see the pavement at all, you're still on it and not in the grass.