How can Madara's Rinnegan be stronger when Nagato has experience with those years for over than 20 years? Simply, look at Obito, who uses those eyes for a day and has yet an Outer-Path which level exceeds Nagato's by far. As someone who got the Sharingan transplanted will never match a true Uchiha who mastered his Dojutsu, an Uzumaki who got the Rinnegan transplanted will never match the power of a true wielder, containing Uchiha and Senju power at its maximum, what directly increases the power of the Rinnegan intself, that is a result of those powers, and allows to use new powers as well as old on a far larger scale, what was proven by Obito's Outer-Path usage and probably by Madara, who easily dropped meteors from the heavens.
It would be absurd if Hashirama alone could match Madara's new powers, that now include a large scale Mokuton and even the Rinnegan on top of the power that made him actually be equal to Hashirama, marginally inferior.
I mean Madara and Obito alone are facing the whole alliance, consisting out of about 30.000 Shinobi that were boosted by Kurama's chakra and include the four Hokage, Naruto, Sasuke, Orochimaru, such as the high tier Jonin like Kakashi with Kamui. It would be a rape to the point it's not even funny if Hashirama is already superior to Madara, and I think this is not how a final fight will look like.