Does Mewtwo-EX's Damage Change exchange or move damage counters?
The wording says "Switch all damage counters on this Pokémon with those on your opponent's Active Pokémon". The word "switch" indicates it's exchange. So your interpretation is correct.

Example: Mewtwo has taken 50 points of damage, while opponent has taken 20 points. After using Damage Change, Mewtwo has taken 20 points of damage, while opponent has taken 50 points.