I thought it was obvious that the meteorites stuff was Rinnegan. From my analysis, all the Sharingan power are confined withing the user. I mean Sharingan does not interact with external objects as weapons. Rather, all the weapons connected to sharingan are internal or attached to the user himself. As for Rinnegan, it has power over everything.
Another interpretation I have from my observation is that Sharingan power is the power of a malevolant god as far as Narutoverse is concerned. I think Rikudo used to be the rival of this malevolant god, and after Rikudo's death, this god corrupt his descendent to destroy Rikudo's will. Well, this is my analysis.
I also think Rinnegan does not make its user a god in the literal meaning. The prime effect of Rinnegan is to grant omniscience. The instant someone obtain the Rinnegan, he has knowledge of every jutsu in the Narutoverse including the sharingan arsenal. However, in order to use all these Jutsu, there is an individual requirement that varies from one person to another. This is well explained by what Lee said to Sasuke:
" Your eyes can give you the insight, but as long as your body cannot follow, it is useless".
This sentence summarizes the difference between Rinnegan users. For example, right now, Madara cannot perform Rhinne Tensei because he has no life force since he is already dead. This where he needs obito. Based on this analysis of mine, I believe that Rinnegan is at best not an Uchiha thingy. I am pretty sure that Rinnegan is a very rare dojutsu among either the Uzumaki (at best) or the Senju (on a lesser extent).