The better passer who has a quick release and reads will make this offense run better overall.
That being said, both guys have the tools needed to unlock the entire offense.
CJ Carr actually has decent wheels. He won't run a 4.5 in the 40, but he can certainly scramble when the opportunity is there. He won't be a stone statue the likes of Tommy Rees or Drew Pyne.
Looking back at the last 15 years:
2010 - Dayne Crist could run the full offense, but calling that many QB runs led to a blown out knee that he never fully recovered from.
2011, 2013 - Tommy Rees could run about a third of the playbook. I'm not joking either, since the only two areas he did well in were the short passing game, and being quite good at making pass protection audibles. He was so slow, that even Jimmy Clausen with a badly torn ligament in his foot in 2009 was faster.
2012, 2014 - Everett Golson had the tools to run the whole offense, but in 2012, he was simply asked not to screw up, and in 2014, he lost his mojo after the FSU game.
2015-2016 - Deshone Kizer could run the full offense. Brian Kelly wouldn't let him at times, and insisted on letting Malik Zaire have a shot at the starter's position in 2016.
2017, 2018 - Brandon Wimbush had all of the tools, but his short range accuracy was terrible, and after he had the yips, got even worse.
2018 - 2020 - Ian Book could run about 75% of the playbook. Great at short and medium range, good runner, and one heck of a smart guy when it came to pass protection audibles. If he had a stronger arm, he would have been drafted much higher up, but with his below average arm, the downfield passing game was limited to medium range throws.
2021 - Jack Coan could run about 70% of the playbook as well, with less of the running, and more of the passing. He could actually throw a decent long ball, but with the patchwork offensive line in play along with Tommy Rees' attempts at being Brian Kelly, the downfield passing game wasn't there.
2022 - I honestly don't know how much of the playbook was at Tyler Buchner's disposal. There's no doubt he could run the ball, but his passing skills nearly gave me a heart attack during the Gator Bowl. Drew Pyne was a lot like Tommy Rees, that he had very little mobility, a weak arm, etc., but was worse that he wouldn't look anywhere but the right side of the field where Mike Mayer was.
2023 - The whole playbook was available with Sam Hartman, but the receiving corps left much to be desired. If Coach Freeman had brought in a legitimate WR1, I think we would have made the playoffs.
2024 - I'd say that about 50% of the playbook was available with Riley Leonard at the beginning of the year. Once he learned to how be a better throwing QB, 70% of the playbook was available.