Many men in Denmark around my fathers age (late/mid 50's and start 60's), support Liverpool. The reason for this is because they grew up with something called "Tipslørdag".
This was basically just Saturday being the football day and many games from the English First Division being shown in TV, it was so nearly every weekend. And as so many came to support Liverpool as they were kids/teens/young men in the 70's and 80's and grew up seeing Liverpool being the dominant force.
You also have those that support numerous German clubs, Bayern and Gladbach was very popular also.
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Liverpool is for sure bigger. The only reason this is even a debate is MU's insane marketing success and Pool's 30 year failure to win EPL, which influences the perception. But objectively Liverpool is bigger.
I'd take these United legends:
Van Nistelrooy, Paul Scholes, Eric Cantona, Roy Keane, Japp Stam, Schmeichel, Van der Sar, Ryan Giggs, David Beckham, Vidic, Ronaldo etc.
Over these Liverpool legends; Suarez, Torres, Gerrard, Dalglish, Allan Hansen, Souness, Mcmanaman, John Barnes, Michael Owen etc.
Honestly I got a hard time listing Liverpool legends as I feel they're lacking those GOAT players. Sure they're having legends, but how many can we say are in that GOAT category?
What Liverpool got on United is their proud history in the European Cup.