To summarise what others have effectively said, you'll get no noticeable improvement from either. It's a bit like asking which of the following will improve your car's performance: A "turbo" sticker on the back of your car or painting flames down the side. This is not an accurate analogy though, because unlike the audiophile world, neither turbo sticker manufacturers nor car painters claim their products actually improve performance!
BTW, also as mentioned previously, all commercial recording studios run balanced setups because they're typically high interference environments which also require cable runs of several (or more) tens of metres, so the noise rejection properties of a balanced setup typically have an impact. Your headphones probably have a cable length of only 3 meters or so and are used in a low or moderate interference environment, therefore no audible benefit.
G