I wouldn't call this proof exactly, but I believe this hypothesis is correct.
Both Obito and Madara have essentially represented half of the Sage each (dark side), as humans.
Obito embodied the actions (some directly opposite) and ideals of the Sage, gathering the bijuu's, creating war, completing the events that led to Naruto and Sasuke's bonds, also worth noting that Obito cares about bonds himself and is why he wants to deny reality. He has also been the narrator for everything we know about the Sage and the Sons until recent chapters. Let's his feelings decide his actions.
Madara embodies purely the power and knowledge of the Sage, he holds the power because he essentially usurped it from Obito, however, he is much more adept and wise than Obito at using the power and completing the plan. Much more heartless, does not care about bonds as much, and let's his mind decide his actions.
Both have become half senju half uchiha, each hold a single rinnegan as Jin, and Obito has the Yang staff while Madara has the Yin. Only Obito so far as learned from the Younger Son that cooperation is the key to the greatest reality.
There are much more things that you can analyze than the staves, and I've made some outdated theories but they still hold up decently for Obito representing part of the Sage.
Both Obito and Madara have set the stage for the fight between Younger and Elder Son to occur again, like the Hagaromo.
