I think you're honestly wrong, in my opinion Real Madrid gives more importance to the Champions League, in fact the season in which Barcelona won (two years ago) they actually abandoned La Liga to focus on the Champions League. I don't know about Manchester City, but for Real Madrid the priority is the Champions League.
Real Madrid abandoned La Liga in the last two seasons because they were not in better form, Ancelotti believes that their strength was not enough to win La Liga and the Champions League in the previous two seasons, so they gave up La Liga and focused on the Champions League; at the end of the season, Real Madrid was unable to win a single trophy because in the Champions League, they were eliminated by Manchester City in the semifinals. Real Madrid performance last season showed that the Champions League was not their top target, they focused on every competition, which is why they won as many trophies as possible.
However, if Barcelona get the players they are about to sign before the start of next season, they will have a chance to win La Liga over Real Madrid, they must be consistent with their games, not like how they were last season when they lost to weak teams. I believe they will be able to defeat Real Madrid next season and win La Liga, but they will not be able to win the Champions League.
How about now, Real Madrid are currently in their best form they would ever wished to be in other for them to compete for as much titles and I don't see any chances of them losing the La Liga not even to Barcelona who has been the most contender. Barcelona are still building up their team with new players/coach and a lot of mistakes would be made causing them to lose points unlike Madrid that is already balanced. Mbappe seems to have blended too quick with the team making them already perfect and a bigger threat especially in the La Liga.
Barcelona are not even close to win the Champions League, seems not even Madrid aswell but Manchester City are up to their game this time, and they just the favourite to win it this time.