I don't think there's any question about it, on the transom!are you going to lay it in the bottom of the boat while you're out on the water? Not only do you have the weight of the motor on the transom while in the water, you also have the force of the motor pushing against the transom while under power.
You'd prolly be less likely to damage something on the motor with it on the transom... prop, tiller arm, cowl....
Outboard motors are meant to be kept in an upright position.
Just my thoughts.