It is a pity that they are playing against Manchester City because I think Manchester City really is out of their league. I absolutely agree with you that they have shown some astonishing and surprisingly good performances in the Champions League. With some luck they could have gotten a few more points during the group stage even against Bayern Munich.
I was hoping that they would get one of the weaker opponents in the knockout round of the Champions League, but Manchester City is 98% their final destination in this tournament.
Copenhagen is more likely to lose against Manchester City. But since this is a goal ball game, nothing can be said for sure.
Copenhagen's performance in the group stage was good. And they have proved that this team is in no way to be underestimated. If Manchester City can continue their great performance this season as well as last season then I would say City will win against Copenhagen. However, Manchester City's performance has also been somewhat erratic and weak this season. However, De Bruyne has been included in the squad after a long injury layoff. But we are still not sure if he can play well. So it's going to be tough for City to win against Copenhagen.
I think Copenhagen proved what they can do by getting out of the group. So we should not say that Galatasaray would have done a better job or something because they also beat Galatasaray in the process to get out of the group.
They had to defeat Manchester United as well. But I think even if Galatasaray had qualified instead of Copenhagen, it would not have mattered that much. Manchester City would have destroyed them anyway.