If Manchester City is considered as favorite team for English Premier League or Champions League then Real Madrid must be considered as favorite team for La Liga and Champions League.
Belief is belief but the realistic is Real Madrid are leading La Liga with big differences against Barcelona and Girona but Manchester City don't have a leading position in Premier League. They are under Arsenal and Liverpool in Premier League with less points than two competitors, even difference is not big but their position is not similar to Real Madrid.
In Champions League, they are both candidates for the title this season but they will have to face with each other and eliminate each other to go to semi finals.
There is no doubt that Real Madrid is one of the best club level teams. No other team has won more Champions League titles than Real Madrid. Last season unfortunately real madrid lost but this season real madrid has more chances to win. This season Real Madrid has formed a great team with young players and it is believed that Real Madrid can definitely beat Manchester City in the Champions League this season. The La Liga title is all but assured for Manchester City, all that remains is to do well in the Champions League tournament.
Last season, Manchester City won over Real Madrid and went straightly to their fist Champions League title. It is their first title in history and in total Champions League titles, Manchester City can not compare to Real Madrid but in this season, they are defending their title and want to repeat success of Real Madrid. Defending a title in Champions League is very challenging task and in history, only Real Madrid succeeded so far.