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.
Barcelona are no longer considered top competitor for the UCL because they've failed entirely to bounce back to their feet in major tournaments. They can't prove themselves worthy enough to face the top elite clubs. While Real Madrid have focus and priorities to meet every season. Los Blancos have everything to worry about and winning becomes very compulsory for them. Carlo Ancelotti is here to make sure they achieve the ultimate goals which is been set out for them. The UEFA Champions League have been their main priority every single time.