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.
And there’s jackshit that’s actually good for stopping a bullet without weighing too much. I’m still waiting for my MJOLNIR or Iron Man 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.“
I disagree. I would say that when it comes to sword fighting and fencing with single-handed swords, if you use asymmetrical armour, what you want to protect is your closest target to the enemy, which is your leading hand/arm, typically the right one, not the left – like the silly musketeer pauldrons on that TV show.
We see this in the development of safety gear in various forms of fencing arts, such as mensur, or other asymmetrical modern equipment such as quilted coaches sleeves and fencing plastrons, where the default position is on the right arm or right shoulder/side of the torso rather than the left.
That’s a good catch. I wasn’t thinking about duelists at all, and was talking about medieval plate designs. Armor is designed and evolved to deal with the specific combat situation it faces, and this is one rare case where the priorities are reversed from mass medieval warfare.