You'd probably need to make a determination of the skill of the players. A very strong player vs a novice could be scholar's mate most of the time.

A very strong player would show the novice the scholar's mate once and then move on to hanging tactics and pieces on purpose so that the novice starts seeing things, probably leading to positions that are a lot more rare.

Yes, the stronger the players, the more often they will both go deeper into established theoretical lines that have been played before.