He is a quarterback who relies on big plays and scrambles. He thinks he is Payton Manning but in reality he is more Randall Cunningham. The Patriots Head Coach compared him to Roger Staubach all the time. The offense Carroll ran played to that strength. It's simple, features running the ball on early downs and had very few short passes, especially over the middle.
The Denver offense is one that should be played on time. It requires the quarterback to win by making decisions quickly. This is not Wilsons strength. He holds the ball longer than nearly any other QB. He tends to lock in on a target. If that target is not open, he holds the ball until he can flee the pocket and play schoolyard football. He is great at throwing on the run, and making deep passes. Carrol's offense allowed for that and emphasized running the ball, and throwing deep.
The same line that supposedly could not pass block, was responsible for some fantastic running. The only constant in all the sack the last 10 years was Wilson's refusal to throw the ball on time. The line was not bad. In fact, many of the same linemen who were disparaged in Seattle had good careers elsewhere when they had QB's who would throw it quicker. He now is in Denver and he is being sacked at a super high rate again. Carroll was able to limit the negative sack plays by running on early downs effectively and wearing down the defense.
In the end, Wilson whined himself out of town. He hated the offense that did not let him throw it 40 times per game. Caroll let him play hero ball at the end but he wanted to be a hero all the time. Unfortunately for him, the offense he blamed for not being even better may have been the only offense that he could win with.