I've seen and worked for both. Kind of a catch; a CP that can fly the line (and do it well) as a leader is going to get lots of respect but may fall behind on paperwork. On the other hand a CP that doesn't ever fly will be up on his paperwork but may not have the respect (unless previously earned) from the line pilots.
Really, the CP position is a desk job. As a young pilot I always thought that I wanted to be a CP....now, the only way I would take it is if I coulndn't fly the line competently anymore.