I don't think there's any point comparing AIA with Metallica songs and claiming one is definitively "better" than the other. They're different styles of music, guys. Metallica are/were a thrash/speed metal band, DT are prog metal. Now I'm guessing that the majority of us here are more inclined towards the proggier side of things, so clearly we are going to take AIA other many Metallica tunes in many cases. But that's just because, as prog fans, we find that particular song more palatable.
Yes, AIA seems to be clearly Metallica-inspired, and similarities exist. Still, there are many progressive elements in there that you simply wouldn't find in a Metallica song. Ergo, I don't believe a direct comparison is called for.