RE: O(1) versus O(some-function-of-total-number-of-transactions):

Yes, it will depend on whether or not the number of differences goes up as the number of transactions goes up.

The incentives align so it is in everybody's best interest to make the differences as small as possible. I wouldn't be surprised if that causes innovations to drive the actual size to O(1) minus an increasing constant, as code gets better at predicting which transactions our peers do or don't have.