I've followed Christensen for many years, as a Danish national team fan with a certain preference for players who play the 'beautiful game' (Laudrup was at his peak in my childhood when I started watching games). Christensen is a very elegant CB, both in his physical stature and his game.
Christensen started out as an attacker, and he is surprisingly good at dribling, several times I've seen him carry the ball on his own all the way up the field, when he couldn't find someone to pass to in the midfield. Typically, in those situations, he almost looks surprised himself, because he is an extremely disciplined player who does what is asked of him, and he has been a CB for most of his professional career, so naturally he focuses on defensive duties, and he shows little desire to show off or be a flashy player.
I can see how one might interpret his game as such, but it's a misinterpretation. Like I said, he is disciplined and he plays with a high level of concentration, and puts effort into playing every ball the best he can (and fwiw, I think he sometimes gets mentally tired because of this). Related to that, he is definitly not a high-risk player.
Also, what you will see, and I saw it several times during the Rayo-game, is his patience. Yes, he can frankly be a bit boring in his sideways and back passing, but if you looked closer, you would notice that he waits for the right moment to play the ball forwards, and several times he made extremely precise balls up the field. If there is a lack of passing opportunities, his patience will not be broken, he will comtinue to play patiently.
Having said that, if Xavi asks him to play with slightly higher risk, and to move the ball forwards on his own more often, believe me, he can do it. But that's not what he has been focusing on in recent years.
Naturally, Barca is a team with a very attacking spirit, so Christensen may not be appreciated by the fans for his discipline and patience, and so I'm not too surprised by some of the negativity in this thread. Still, as a fan, I tend to support new players and to give them the chance to show what they can do as they get more settled.