I think they're fighting over it because Obito wants true peace and he wants to be the one who brings this true peace. He wants to be recognized as the one who revolutionized and changed the Shinobi world, this probably stems from his childhood desire to become Hokage which he ,it seems, still wants to do as seen in the last few chapters.
On the other hand I think Madara just wants to be at the top. He stopped caring about the world and rage quit here
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when he says
"It'd be better for us to look at this world as just entertainment..." so I don't think he cares too much about bringing about peace (and he couldn't careless about the Ninja alliance because nobody he knew or cared about is necessarily alive), I personally think he's just letting in to his God complex and wants to be god because if you notice he mentions being at the top a lot like
here:
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and here:
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So you could say Madara is a little childish... but I think it's kinda cute ....