Ok, let's estiguess the shit out of this one.
American Revolution.
There were about 265 notable battles.
https://en.wikipedia.org/wiki/List_o...ry_War_battles
The most number of American Soldiers on the battle field at any time was about 13,000. Most battles would have far fewer. Let's call it 2500, with another 2500 British.
Soldiers typically carried 20 to 30 rounds, but a typical battle using tactics at the time would consist of a few volley exchanges, followed by bayonet/hatchet charges. Let's call it 10 rounds fired per combatant per battle.
https://www.ncpedia.org/history/usrevolution/soldiers
Max upper limit might be 265 battles*5000 combatants per battle*10 rounds per combatant = 13M rounds
American Cinema
Estimates of the number of American movies range from 50,000 to 500,000. Assuming Rain Man is referring to the narrower range of movies (defined as having an MPAA release number or appearing on IMDB) there have been around 50K movies made.
So taking our 13M rounds and dividing by 50,000 movies gives us a break even of 265 rounds fired per movie. As a reference point,
The Matrix (a movie with above average automatic weapons fire) had around 2000 rounds fired. Clearly it is on the high end of distribution of all American Movies.
On average, I'm fairly confident that there are less than an average of 265 rounds fired per American movie, but it is in the ball park. The number of rounds fired in the American Revolution is probably a high estimate. Still, I am going with the estimates here, and going to say more rounds were fired in the American Revolution, but would not be surprised either way.