ISTM that the first of these are much less relevant stats, as they are heavily influenced by the clock. The second are what counts - how your offense/defense directly stacks up against the opponents defense/offence.
But there is a lot of focus on the first of these and I never hear the second mentioned.
[In light of the above, I think the Jets, for example, have an overrated defense, since their offense focuses heavily on the run, and they likely defend far fewer possessions than many other teams.]
Football and Basketball share a similarity in that the team on offense has a variety of strategies to choose from that can affect the pace of the game, and there are relatively few turnovers. I agree wholeheartedly that points per possession is a far more useful indicator of offensive/defensive prowess than points or yards or FG%.
I don’t know if it’s compiled anywhere for Football, but for Basketball you can go here and look under Miscellaneous Statistics, called Offensive Rating and Defensive Rating, which is points per 100 possessions. However, they call it an estimate, perhaps there isn’t a strict accounting of # of possessions?
I believe the issue is free throws. Without knowing exactly what led to all of a team’s free throws (defensive 3 seconds, technical fouls, and-1 fouls, and just plain 2 shot fouls), you have to estimate how much a free throw is “worth” in terms of possessions. Most estimates are that a free throw is worth 0.44 possessions, AFAIK.