Best Capital Ship for My Team - Tarkin or AA?

You don't really have a fleet. You can build whatever you want easily from this point. I suggest starting with characters you plan to use long term throughout the game. Level, star, mod, and gear them, which will increase their ship. Some good advice was given already. I'll just add my experience. I take first regularly, depending on who snipes who last. I use mace, against aa and tarkin fleets that are significantly more powerful than me. It's all about target lock. Build a fleet of target lockers, and let mace do his thing. There is no team I can't beat, but a few can beat me, because AI uses mace very poorly. In the end, no one capital ship is best. Farm the ships of the characters you use, and take it from there.