There has been some historical buzz on the Internet (weird, I know!) about the hypothetical question of who would win between a Marine Expeditionary Unit vs. the Roman Empire during the reign of Augustus, which is a close approximate for Rome at its zenith. Technology and troop levels have predictably been the main focus of conversation. I like these kinds of questions, especially since I'm covering ancient Rome with my 9th graders right now, so I just want to toss out a few thoughts.
The technological advantage is obviously on the side of the Marines. Really, the whole question is about measuring how much more powerful we are in the 21st Century than the most powerful nation on Earth during the 1st Century was. This will be the key to obliterating support for Augustus, as the first Emperor will appear, and in fact be, impotent to stop the oncoming invaders. Nothing surprising here.
The question of who would win, however, requires parameters in which victory is defined. Could the Marines overthrow Augustus and institute anarchy? Unquestionably. They could shell the Palatine and Capitoline Hills from miles away from the city, potentially wiping out Rome's leadership instantly. But could the Marines supplant Augustus rather than merely obliterate society?
I believe the answer is yes, but there are two important variables. For starters, the Marines would have to set out immediately with the intent of supplanting Augustus. If this is some sort of time traveling invasion and this is the mission, the Marines are dedicated to this objective, then I believe they will be in very good shape. Without a clear mission, however, the Marines will use up their supplies very quickly without achieving anything. Food and potable water will be far more important than ammunition. The Reddit version has the Marines magically being transported back in time and space. In that situation, the Marines would need to very quickly decide to take over. Our soldiers are extremely good if there is an objective, but without any objective, confusion would reign. At that point, it's not even Romans vs. Marines rather than Marines trying to figure out what has happened while being harried by Romans. The question is a lot clearer when both sides are intentionally trying to take the other out.
The second variable is whether any of the Marines speak Latin. Back on the website I linked to, I'm kind of shocked Adrian Goldsworthy believes the Marines would lose due to a lack of numbers. I've read Goldsworthy's book on the Punic Wars and saw striking similarities to our conflict in Afghanistan. The trick is to win over individual cities with a carrot and stick approach. If the Marines can communicate and win over those socii, they suddenly have the manpower to enforce peace in Rome or in any other city they choose.
Of course, we'll never know, but it certainly is an interesting question.