Edo Tensei is a literal 'Ninja Zombie' and is clearly a crappy existence for even the person brought back even if they are practically indestructible. Rinne Tensei comes at the cost of the user's own life force.
Also both techniques either require a sample of genetic material(Edo) or the whole body(Rinne). While nobody knows what happened to Rin's body, it's clear it may have been reduced to ashes which is standard operating procedure for ninjas like Rin because bodies can give up secrets. In her case it can be said it had to be destroyed because of her closeness to Minato(Uber Powerful) and Kakashi(ANBU Captain/Black Ops).
Also Obito was frickin' nuts. It's been shown that Edo Tensei people can be stopped and being brought back by Rinne Tensei does not guarantee immortality. So Obito in his madness chose an undying illusion of Rin.
