I don't think that City are so fed up with EPL titles that they are ready to put the Champions League higher in their priorities. Maybe if they had a guaranteed choice between these two titles, they would choose the Champions League, but there is no such choice, and even reaching the final, you can lose everything. In terms of reliability, the EPL looks much better, especially when your team is in the lead, albeit by a small margin.
City and Liverpool both have busy schedules, they have to play in 3 different competitions, UCL, EPL and FA Cup. Perhaps, the trophy that is not a priority is the FA Cup. the rest they will try to be able to bring the remaining two trophies to the clubs. I'm not sure Liverpool only want to focus on one trophy, neither does City. They will focus on 1 title if they have been eliminated from the FA and UCL. if not, it looks like UCL and EPL are targets for them.
Pep guadiola will be very happy to give Manchester City the champions League before he leave England,is the only trophy he has not won for Manchester City,infact since he left Barcelona he has never won the champions League,all through his time at Bayern Munich (Germany)he did not win it. so I think he will be obsessed with it and would love to win it at City,with the type of squad he has he should be confident,but that does not mean he is going to surrender the premier League to Liverpool, we all know that he is a winner and would love to win everything.