Historically…difficult to answer… Both went through periods of massive success, which are behind them now. Both have passionate fan bases.
Commercially… without a doubt united. Manchester united is a commercial juggernaut.
Currently as a team I’d go for Liverpool, they’ve a manager that fits with the club’s identity. The team has a solid core of players. Whereas United have a misfit of a manager whose philosophy to the game clashes with the one that fergie built over his tenure. Big money signings with huge egos (including the manager). Failure to integrate and develop talented young players who’d be united through and through (Martial, Rashford). ManU seems to be in a soup and looking like trying to fix their problems by throwing money at it.