Board Thread:Theories and Speculation/@comment-1512913-20150827121154/@comment-5407586-20150827123912

Hagoromo's chakra is the combination of Indra's and Asura's. Madara/Sasuke have Indra's chakra, Hashirama has Asura's. Itachi and Izuna, while not being Indra's transmigrants, are still his descendants, so I think their chakra can be considered as an extension of Indra's. So, in the end, Madara and Sasuke's Rinnegans would be the result of Hagoromo's chakra gained by combining Indra's and Asura's.

It's just my idea, but once a Mangekyō Sharingan gains eternal light, it can't change powers and design anymore, just evolve to the next step (Rinnegan, obviously). Madara commented that Sasuke's Eternal Mangekyō could've been a good substitute for his Rinnegan, which might point to what I said before.

Izuna and Itachi being more skilled at using EMS/Rinnegan gained through their original eyes? I don't really think so. Even for switching between EMS and Rinnegan: Obito, who was an Uchiha, couldn't switch his left Rinnegan to Madara's EMS (though it's true he wasn't the original owner of the eye).