A Central Midfielder is a jack-of-all-trades - rather than a specialist Deep-Lying Playmaker, Ball-Winning Midfielder, Box-to-Box Midfielder etc. To my mind, he's like a less dynamic Box-to-Box who performs whatever part of that role happens to correspond to his current location on the pitch in relation to the play, but without the imperative to get up and back to become more involved in attack or defence.
If I'm right about that, then it would stand to reason that a CM wouldn't need to have quite as much Stamina as a Box-to-Box, and he wouldn't score as many goals - unless he's aces at heading from set-pieces or smashing it from 25-yards.
I'd expect to use a CM in the lower leagues, where I might not have players good enough to play the specific roles that I want, or if I had a World Class player who was equally excellent in any one of several midfield roles. But I prefer to use specialist Deep-Lying Playmakers, Ball-Winning Midfielders and now a Regista to control midfield and get the ball to my attackers in dangerous areas.