If you're comparing the run games of the two teams since the 08 draft, it's worth noting that Atlanta had a better rushing attack in 4 of those seasons (2008, 2010, 2015, and 2016). Now, whereas that does give Flacco the lead with 5 years of having a better rush attack, one of those 5 years was 2013 where we all know that rush offense was pure trash. We beat out Atlanta in yards per game, but they had the better ypc (3.1 vs 3.9) and more rushing TDs (7 vs 11) so I'd really call that a wash as both rushing offenses were....offensive. So they both sit at 4 out of 9 seasons with a run attack worth mentioning that was better than the other's.
In terms of any debates between the two, it really comes down to one thing to me. I feel both would have still made the playoffs a bunch of times if they had swapped teams, but I still think Joe would have played better in the playoffs (I'd assume nobody thinks he'd do worse, performance wise, with all the Falcons talent over the years). And I just can't see Joe losing yesterday with that offense. I can't see Joe being unable to lead that offense to more than 1 score in the entire second half, not while having a WR make circus catches and another that was breaking ankles on the field as if this was the NBA.