What are ya talking about?
Rinnegan is the evolution of the Sharingan, it's already been said in the manga.
It has sharingan abilities + rinnegan abilities.
So it's better than sharingan.
Look at Madara. He's the one that awakened it, and he's both sharingan and rinnegan feats with it.
EMS Madara vs Rinnegan Madara?
Both with Mokuton.
Then it would just be called the Ultimate Sharingan instead of the Rinnegan. It has a different name because it is a different eye. It is more powerful for sure, but since it is actually complelely new eye, instead of being simply an upgrade like EMS, the user will need much more time to be adjusted to it. That is why Madara couldn't find a reason to replace his PS. He simply didn't master the Rinnegan because he simply didn't have it for that long.
Nagato? Well, the eyes aren't his. And, quite frankly, Rinnegan eyes aren't suited for anyone lower than God Class( S06P, Madara, Hashi etc).
If Madara had the Rinnegan, in his prime body, for say a decade, he would easily find an excuse to discard his PS in favor of more powerful Rinnegan techs.