Here's my two cents:
For ordinary on-road trailering, it probably doesn't make any difference to the transom, which is strong enough so that it doesn't make any difference which way the motor rests.
If you're going over a really rough and long section of road that will make the boat pitch up and down by the stern, it would make more sense to choose the position that would minimize the effect of the pitching of the motor on "working" the transom back and forth.
So would that be up or down? Up puts the motor's center of mass more up and balanced over the center of the transom, while the down position puts it aft. Which one will minimize the working motion? Before we get lost in the analysis of the dynamics of this question, we can look at one other factor, which makes this question moot.
That would be the possible wear and tear to the tilt and trim hydraulic cylinders and systems. To minimize the thrusting and wear and tear to these, one should tilt the motor up, engage the lock in the up position by dropping the lever down in place, then use the hydraulic trim control to lower the engine down so the weight rests on the lock mechanism and there will be no pitching motion transferred to the hydraulic cylinders.
Considering the overall strength of the transom and the very important, perhaps over-riding need to protect the trim and tilt mechanisms, the up position wins.
To me at least, leaving the motor down on very short trips with flat roads would be OK, but I'll always tilt it up and lock it on longer trips, knowing that the hydraulics are fully protected and I'm ready for any kind of road condition to be encountered. Joe.