I think the main reason why Milan AC performs much better in Serie A is because most Italian teams handle the same style of play, they know each other very well and obviously the one who plays the best game will reign
Champions League is different than Serie A, more competitive and you are right about difference in tactic, style of play. Once more, players always have pressure when they have debuts, in a new club, a national team, or Champions League. In reality many players of AC Milan have their first experience in Champions League so I don't expect all of them can play well there.
when compared with the CL everything changes, it is a clash of styles of play, obviously it is measured which is the strongest and the most effective, of course I remember the Milan of Paolo Maldini or the one with Kaká, who had a level totally adapted to the league already the CL.
The time with Kaka and Paolo Maldini, AC Milan had very experienced players and they are one of best players in their positions, from defense to attacking. It is like one of dream teams in Europe with Maldini, Costarcuta, Nesta, Cafu, Gattuso, Pirlo, Ambrossini, Seedord, Kaka and Shevchenko.
Don't forget that they also had Stamp, Crespo, Inzaghi and few great players. Now, they are coming back and don't see their failure in this season as too bad. It's just the beginning for AC Milan to return to their giant position in Champions League.