They usually outplay the other top teams, in fact they do that more often than Liverpool. For example, they have completely outplayed Tottenham earlier in the season, yet somehow Spurs managed to conjure two goals from zero chances. While vs Liverpool they miss open goals.
Not to mention City had a goal disallowed by a marginal call at the end of that game. The same type of call was interpreted differently and had them out of Europe months earlier, because the rules still had not been changed then. And it was against the very same Spurs, who conceded obligatory ridiculous goal at the beginning of the final, you guessed it, vs Liverpool.
As for City vs Liverpool matches. In the most recent one, City have a penalty call ignored, have players stop playing, and Liverpool scores a belter on the counter. City create more and have control for most of the match, but Liverpool score as soon as they cross the half. These are the margins in question.
These are not isolated examples. The same pattern usually repeats in other matches. I have recently compared Liverpool with Juventus of recent years, and someone also did on the other thread today. Same kind of plot armor in the league, even more ridiculous. There's a reason why bookies still have City as favourites in Europe over domestically "dominant" European champions. They're still a better football team.