All of Carl's moves himself are on key-down.
So think of what your fingers must do to consistently pull off combos like: https://youtu.be/D8gPPB9YD6s?t=65
You get the benefit of playing two-characters vs the opponent's one character, but it means having to think about both characters (as well as having a wonky control scheme for the 2nd character). Furthermore, Carl is designed to play with the doll, so you only deal the same damage as everyone else if you successfully pull off these combos.
But having two-characters means you can setup unblockables more easily (doll hits high, Carl hits low), or weird pressure strings / frame traps that are unavailable to most typical characters. Which is where Carl's unique advantage really comes in. So its not a "damage" thing, its more about the mind-games you play with the opponent when its 2vs1.
Terminology: A, B, C, and D are the four attack buttons in the game. Numbers represent which direction you push (2A means A-button while holding "Down". 2 is down on the numpad. 8 is up, 6 is right, 4 is left). Every fighting game community has invented their own terminology. But knowing this should give you enough information to watch that combo-tutorial adequately.
A, B, C map to Carl, D maps to the doll. Holding D means that the doll starts to move left-right (4 or 6 with your left hand), letting go of D means that the doll attacks (negative edging). A, B, and C on Carl play as a typical fighting game character.
Carl is... not easy... to play.