If all else is equal the damage dealt is proportional of the Attack stat of the pokémon.
Every pokémon has 3 base stats: stamina, defense and attack.
Each of them is multiplied by the same factor. And this factor increases as the pokémon is powered up.
In the CP formula the stamina and the defense are square rooted factors and the attack is a linear factor.
This means doubling all stats results in 4-fold increase in CP.
So if all else is equal an 1200CP pokemon causes twice more damage than a 300CP pokemon does.
But keep in mind that damage is not everything. You can have a pokémon with low damage but high defense and stamina which is more successful than a pokémon with high damage but low defense and low stamina.
A pokémon with twice more attack serves twice more damage, so it's twice more powerful.
A pokémon with twice more defense receives half damage, so while it lives it can serve twice more damage, so it's twice more powerful.
A pokémon with twice more stamina has twice more hit points, so it can withstand twice more punishment, so while the hp bar depletes it can cause twice more damage, so it's twice more powerful.
So to compare the true combat potential of a pokémon specy, multiply its base stats.