Who deals the most damage

If you can, buy the IAPs. Wellesley, Napoleon and Blucher deals some incredible damage.
Lets assume you are only doing free to play which means no in app purchases.
Cavalry, maxed cavalry generals deal the best damage in the game, and what's better, being able to attack more than once when an enemy is killed. If you're not going for blucher, go for murat and dabrowski, max that aura and precision strike skills. Lan the princess is also good, max her precision strike and edge to eliminate infantry. Maybe davout or paget are contenders, max the tactic master skills and always max the precision strike for every cav gen.
Artillery, artillery unfortunately can not eliminate enemy units in one go but they can destroy up to level 3 cities in one turn. For this, i recommend kutuzov, scott and especially john. Max their salvo and storm fortification skills, for john, max the terrains skills and then find a mountain or jungle tile or even both and then shoot at a city, he will absolutely destroy it. Remember when i said that artillery cant destroy units, well there is an exception, rocket artillery. For this i recommend mahmud and alexander because of aura and crit, maybe john again, scharnhorst because of plain fighting and inspiration and kutuzov isnt bad too.
Infatry generals can also deal great damage especially with critical hits. Grenadiers and assault infantry are the way to go. Massena, max his assault, tunnel and aura skills to destroy cities and maybe upgrade the rest of his skills to destroy enemies. Karl is good too, emperor title and max the aura, also max his intercept skill to destroy cavalry.
Washington, bismarck and Suvorov are also some good contenders. But i feel like karl and massena will be a little more worth it when you are having medal shortages.
At first when you just buy these generals, they will deal some good damage but not excellent ones, this is where patience to upgrade their titles and grinding to upgrade their skills and ranks and putting items and medals comes into play

This was long