If you only take specs of both battleships into consideration you will undoubtfully find out that the Minerva is equipped with weaponary to destroy other battle ships. While the AA is built for multi-purpose situation mainly for large scale war. Both ships can possibly take out the other if the attacks are concentrated correctly. Therefore both ships are on the same scale in this matter. Except, Minerva is built way after AA therefore it's technology is far more advance to AA, so MInerva has the advantage there. The Tanhauser has a longer range then any gun AA has on it's arsenal. The overall comparison would end up with MInerva winning, but when the added factor of who's the captain then it can be clearly stated that it all results in how much skill and how clever the captain of the battle ship is. Also as stated before somewhere in this forum, there is a theory saying that Minerva's original intent was to be built to destroy AA therefore it is better armed and more manverable then the AA in almost all factors. Except the only thing that the person who designed the Minerva missed out was the new AA was upgraded to be able to dive underwater as it previously wasn't able to in GS. Therefore that's the only disadvantage it has over the AA. According to Episode 43-44 the AA was extremely disadvantaged to the Minerva the whole battle until it decided to use submission tactics to fight back. So, the last word would be that Minerva would win if it was a regular space war of dumb captains and cannon spamming retards.