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.
Maybe this is an advantage for Manchester City because they have weak opponents in the round of 16 and this is also a challenge for Copenhagen when facing the best team in the world. Manchester City automatic strength is superior to them so there is no doubt that the betting house will favor Manchester City in this match. The first leg will be played at home to Copenhagen, but still, if the opponent is Manchester City, then the chances are that Manchester City will win.
Apart from that, Manchester City is the defending champion so it is not surprising that they will be able to reach the next round if you look at the opponents they face in the round of 16. Apart from that, Real Madrid will face Leipzig, where in this match it is very likely that Real Madrid will be able to beat Leipzig. It looks like several matches in round 16 will be easy to predict the final result. I think only Barcelona vs Napoli is difficult to predict because both teams are relatively equal in strength this season.
They are the defending champion but seriously, that has never meant anything to any team in the Champions League. You don't get anything for it. You have to prove it again in every single game that is ahead of you. But Copenhagen can only try to be as aggressive and physically intense as they possibly can. It is all about the physical condition in that game. They can't compete with Manchester City in terms of passing accuracy or dribbling, but they can give Manchester City an extremely hard time to score the first goal and then wait for their chance to score a lucky shot or something.