Liverpool won't be tired more than City, they will both be tired considering how many injuries each team has and how many games they play, things aren't that easy and because of this we need to consider how to get better results on the long run as well. Fatigue is the biggest reason for injuries, I just hope that we do not see players get injured in this game, not all injuries are results of tackles, most of the injuries are done when someone tries something very normal, nothing out of ordinary, just because they tired themselves out too much.
Hopefully, with this situation being so tiresome, we could finally see UEFA and whatever else competition organizations out there, they can see it's ruining football to have this many games, it means more money when you have more games but it also means that you are tiring the players out a lot more and injuring them and that means we actually watch them less now, back in the day there were less games but players were injured less and we would watch them play more games in total.
It will depend on how Liverpool plays the game against Real Madrid. If it comes to a serious battle and Real Madrid pushes Liverpool to the limit, then this could have a minor impact on regeneration. But I doubt even that because the game is on Sunday and it shouldn't be that big of a deal for Liverpool to have fully recovered by then. But I think that Liverpool will have the game against Real Madrid under control and if they score a goal first, I think they will slow down the pace of the game and rather try to maintain than to keep attacking.
They can afford it since they have lots of points already and if that turns out to be the case during the game, Real Madrid would be the team that has to attack nonstop and Liverpool could be concentrating on clean counter attacks.
Manchester City has other issues than just physically recover. They literally need psychological treatment after what was going on recently. Pep Guardiola hasn't found the right words and for the team it would be good to calm down, not beat themselves up and prepare in the best way possible for Liverpool. It is a key game for the whole season.