they dont have more damage. i mostly see the adc either do an equal amount of damage, or more in my games. the only time when i deal more damage over the course of a game is usually when bot lane loses and i win my lane. but to answer your question.
adc:
- high sustained damage against champions from range. proper positioning means you never get touched in a fight its also easier for you to pick or switch targets
- high siege potential. they can take out turrets easier than melee bruisers or melee adc since they dont have to get too close against defenders
- utility. a lot of adc have cc and/or mobility tools in their kit
- highest consistent damage to drake and baron. taking one of those with an adc is usually faster than with anyone else
melee bruiser:
- high sustained damage against champions in melee
- high defense to survive getting into the middle of the enemy team and then dealing damage
they excell in skirmishes and 1v1 scenarios but dont have the same siege potential and are more easily locked out of a fight. the more people are involved in a fight and the more cc is available to rotate against them, the harder it becomes for them to reach their desired target.