When he first arrived at Arsenal he was great. He scored 7 goals in his first season, and it wasn't just heading balls in from corners, he scored a few from open play too. He has good technique and good vision (as you'd expect in a player trained at Ajax) and for a while he was considered the perfect example of a "Ball Playing Defender".
He's a very hard worker, he is a very professional player, he doesn't make rash challenges, he doesn't play dirty, etc.
On the other hand, he's not all that fast and sometimes his desire to get forward and attack means he's caught out of position. He's surprisingly good on the ball for a defender and makes good runs, so it catches people out. If there are players who can cover for him, that works out well. If not... well...
If I heard that Barcelona wanted to have a 3-man back line and they hadn't just bought Jeremy Mathieu, it would make perfect sense. He'd be ideal as a left-sided CB in a back 3. With Jeremy Mathieu's signing I'm not sure. They'd both probably want to play in the same spot, on the left side of a group of 3.
He was made Captain of Arsenal for a reason, and I think he'd still be starting if there had been a fast, cautious CB to partner him. Instead, Arsenal bought a slow, cautious CB in Mertesacker and a fast, aggressive CB in Koscielny, and that partnership has worked out ideally.
Against weaker La Liga teams, he'd probably be a real asset for Barcelona, because his forward runs from the back line would disrupt defences that are parking the bus. He has CL experience, but it remains to be seen if he can get back to the form where he'd be a great starter for Barcelona in the CL