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.
In terms of domestic success, Milan is much further behind Juventus, who have almost twice as many league titles, than Liverpool is behind Man Utd (the difference is just one league title). In terms of continental success, they both have 9 trophies (not counting supercups), with Milan having 1 more UCL/EC. So I’d say that Liverpool is far more dominant domestically and they are on par in European competitons, with LFC being much better overall in the last 10-15 years. Milan did have more all time greats, but they can’t attract players of that level anymore.
I’d say they are clubs of equal status historically, but certainly Liverpool has a bigger status in recent times and is slightly more successful overall (due to Milan lagging far behind Juve in Serie A).
And I’d like to add that it’s quite likely that European record in the late 80s would look very different if Liverpool weren’t banned from competing.