Having a debate with an Italian guy about who is the bigger club and I think it’s close.
Both have won their domestic league 19 times and Milan have 1 more Champions League.
Milan probably have more well known legends like Van Basten, Kaka, Maldini, Gullit and Pirlo. But in recent years Liverpool have had Gerrard, Suarez, Alonso, VVD and Salah.
The current popularity of the Premier League helps Liverpool but Milan also has a huge fanbase.
As I said in Milan subreddit and is always my argument: no logical milan fan would swap their history with any club than Real Madrid.