Liverpool and Klopp will be same like Manchester City and Pep Guardiola. They will both try to win Premier League and Europa League (Liverpool) and Champions League (Manchester City). At this time, they will not try to decide what competition is most important for them as both titles are big ones and they still have due chances to win both titles.
Manchester City look to have better player resource and don't have problems with player injuries at this time and it's big advantage for them in their race directly against Liverpool in Premier League. The wave of player injuries can affect Liverpool performances in coming matches and can affect their endings this season.
For Liverpool, I think there is still a difference, because winning the Premier League will mean much more to them than winning the EL. But for Guardiola, these two tournaments are really very important, because they are the current champions in both and they need to defend this title, if they manage to do this, it will be a very big achievement for City and Guardiola.
It looks like Liverpool don’t have any big problems beating teams in the EL, their level is clearly the Champions League, it just so happened that this season they are forced to play in the EL, and although they definitely have the desire to win, if necessary, I’m sure that Klopp will retain his preference for the Premier League . We also shouldn’t forget about Arsenal, who also want to become champions and at the moment they are in the lead, so we are in for a very exciting end to the season.
It's very true about Liverpool, they are actually the team to beat in the uefa Europa league, because they have proven that their level is the uefa champions league, and I think they have all in their ranks, regardless of injuries to lift the uefa Europa league title.
And as for the premier league, I think as it stands, any of this three teams have a clear chance of winning it, but as a neutral fan I would be giving it to Liverpool because, they have a better fixture compared to their both counterpart arsenal and Manchester city, and another thing is this upcoming fixture between arsenal vs Manchester city, I think the best results Liverpool can get from that particular fixtures is if they can share the point, and with that they will definitely top the league if they can get their desired result against Brighton.