Supposedly you should inherit a stronger version of both MS abilities but it seems that out of the two EMS users we know this is partially true. We can't use Madara as we don't really know what his and Izuna's individual MS abilities were but with Sasuke we see that the ability gift by Itachi was Amataresu and you have Sasuke's MS ability to manipulate Amaterasu but Tsukuyomi seems to have been lost. After Sasuke implants Itachi's eyes and unlocks EMS you being to see Sasuke manipulate Amaterasu on a much larger scale than previously seen.
So from what I can theorize is that each MS has a unique ability Madara/Izuna we don't know (or at least I don't), Shi Sui had Kotoamatsukami in both eyes, Itachi had Amaterasu in one and Tsukuyomi in the other, while Sasuke's unique ability was to manipulate Amaterasu. When Itachi gifted Amaterasu he essentially granted Sasuke his eyes chakra but the full potential and eternal light couldn't be achieved until he went through with the physical transplantation.