Allegri failed when he last coached Juventus before leaving for Milan, so I won't overestimate or set high expectations for them. I think anything is still possible for AC Milan this season. Although AC Milan fans have welcomed Allegri enthusiastically, I'm still realistic.
Competition in Serie A is tough. Several teams have improved their performance, which poses both a threat and a challenge for Allegri.
Not to overestimate him but Juventus is not same as Milan because the experience are going to be two different experiences in different levels with different set of players and different mindset so you never can tell how better it can be at Milan than it ever was at Juventus. I am not trying to hype Milan so much but things does change at different places with the environment and the people there who you get to work with and do not forget that his time at Juventus was one of the times Juventus had a lot they were taking care of but at Milan I do not think that is the case.
I just hope that either Juventus and AC Milan can perform better this season, so the competition for the Scudetto doesn't just involve Napoli and Inter Milan. Allegri might not set the target too high in his first season, a realistic target would be to guide AC Milan to a top four finish to secure a ticket to the Champions League next season.
AC Milan should be able to perform better since they are not competing in any European competitions and can focus solely on domestic leagues, while Juventus will face a tougher challenge. However, this cannot be the only indicator to determine the consistency of both teams going forward. So far, Juventus has had a better start to the season than AC Milan.