Difference between edo tensei Madara with rinnegan and Alive Madara with Rinnegan
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.