Well first season he came and instilled some tactics back into the team after Leonardos 4-2-fantasia formation (four forwards doing whatever they wanted)
Defensively he did improve us as a team but honestly that first scudetto was Ibra, then Thiago silvas. Third I'd say Seedorf and fourth van Bommel.
Second season our squad was still good enough to win the league and honestly, Allegri got it all wrong in several games. A few stick out like fiorentina and juventus. His third season was never going to go great because we had then lost Seedorf,nesta, gattuso, pippo, zambrotta, van Bommel and also sold Ibra and Thiago silva, so the fact he still got us into the champions is actually quite impressive.
I haven't watched much of Juve for obvious reasons because imagine watching man Utd win the league again and again and again you'd just ignore it and try avoid it wouldn't you, so I can't comment on what he's done for them too much.