Difference between edo tensei Madara with rinnegan and Alive Madara with Rinnegan When madara was revived, he lost his pair of rinnegan ,his reservoir of infinite chakra  and not be killed ability (being an edo tensei).

So, I know why madara wanted to be revived, but my question is , how does the ability differ in these 2 cases?
An Edo Tensei cannot be a jinchuuriki, and so, he couldn't complete his plan by becoming the Ten Tails' jinchuuriki. That is the main reason he wanted to be revived.

Also, although very powerful, the power of a "real" Rinnegan is far superior to one of the reanimated "fake" Rinnegan. The "real" Rinnegan can summon and control the Gedo Mazo, use the Rinbo: Hengoku technique etc.