Honestly I have yet to be remotely impressed by the Minerva. Its weapons have all been damaged at one point or another and several times the damage was rather serious. I personally had a Issue in 43 where Neo takes out the Isolde and then later that day with no noteable repair time they are off to space. That completely aside in every battle between the 2 ships the AA has been in a situation where they were completely outnumbered and in several cases in a unfavorable tactical position and the Minerva still couldn't do any serious damage. Yes when the AA was fleeing and specifically avoiding fireing at the Minerva it did damage there engines but that has been the extent of it.

The Minerva to me seems simply to be a subpar carrier ship that at the Beginning of GSD even needed to have Mobile suits on the ship defending it with only one or two units (3 for the one battle with Heine). With which it attacked while 2 suits (rei and Lunimaria) were basically left to guard the ship. In direct contrast the AA is a Battleship essentially made to fight with or without Mobile suits. This to me atleast gives it a HUGE advantage in a one on one battle with the Minerva. Essentially we are compairing a heavily armed battleship to a lightly armed Carrier ship. Note that also both ships are Carriers and I do believe the AA also has a greater storage capacity.