Well the other assault carrier wasn't transporting a hierarch but it was with his fleet, so it could still make sense for it to be somewhat more powerful than average since it indirectly was still protecting him.
No evidence to really support this claim.
Ok the reason that Regret's ship got through is because all of the other ships covered it. Not to mention that Covenant boarding parties has destroyed two out of the three ODP's on top of that Harper's fleet was focused on the other CAS. The fleet was further reduced in firepower do to the CAS's bypassing the remaining ODP. The fleet could not use nukes without running the risk of disabling their last ODP. And remember it to destroy the Covenant Super-destroyer it to 27 ships concentrating their fire. 27+ MAC rounds (some ships may have had double MACs), all of the fleet's Archers timed to hit 0.1 seconds after the MACs impacted, and all of the fleet's nukes timed to hit 0.2 seconds after the MACs impacted. That is a lot of firepower and before that salvo the Super Destroyer was shrugging off hits from MACs and nukes alike. It took everything that those ships had to destroy the Covenant vessel.
It still shrugged off SMAC rounds which deal out roughly the equivalent of 51.6 gigatons of TNT upon impact a UNSC frigate has a standard yield of 64 kilotons. Also the Assault Carrier shrugged off even more firepower from an even larger fleet AND an SMAC and was still whooping the Home Fleet as showed in the cutscene posted. Even once its shields were down they couldn't destroy it until the Chief had a plan.