The Champions league is the toughest league to win, to win the Champions is hard to predict. I think Manchester city puts Premier league first because they are used to the game in Premier league. Last season Manchester City were thinking they would win the Champions League but they missed it at last.
I won't think so, because in the last season when Manchester City did extremely well in both premier league and Champion league there was no such thing as putting a league first before the others especially when the leagues are running at the same time.
Both championship and premiere league are both important for Manchester city, just that this season premier league have been tough for bigger clubs.