Liverpool leveraged their purchase and takes money out.

City purchased outright and sold two tranches of ownership for 25% to Chinese and American investment groups with the funds invested in the City group. They also don't take money out and the club had the good fortune of inheriting a free stadium in which they have made substantial additional investment.

As much as fans of the American owned clubs bray about dirty oil money and sports washing their own club's financial models tend to be leveraged and extractive from football and their team's cash flow. I'm pretty sure the Burnley owners only put in 20% equity with debt service severely limiting player and other investment.