It depends on how much larger, but yes, there are reasons to have asymmetrical armor.
Asymmetrical armor frequently favors the left arm, because your opponent will (presumably) strike with their right hand. Since the left side will take more abuse, and because you’ll need slightly more freedom of motion with your right hand, over-armoring the left was a real practice.
Popular media tends to massively overplay this, with enormous pauldrons that no one could take into combat, but the basic idea is sound. Usually this would simply involve slightly longer plates that provided better protection to the armor’s joints at the cost of range of motion, but there was a lot of variation.
When dealing with firearms, this is a lot less important, but to a very limited degree, the same concept applies. In most stances your off shoulder will lead. Meaning it will be slightly more likely to take a bullet from someone firing in your general direction. Except, so far as I know, there’s no real modern examples. If I had to guess, I’d say it was because modern combat philosophy puts a premium on mobility over protection.