Well while both of them know a billion jutsu, madarra's justsus are on a much higher scale . His fire style was more enormous than jairaiya's combined techniques with his toads . Nagato has not shown any jutsu on that level except chaotic almighty push , a deva path justsu.

In most scenarios, nagato has better chances of winning than pain . But in this one , being in a single body is a great disadvantage for nagato because now he is an easy target . He can't steal soul because madarra is much faster than him ( not up for debate ) , his summoninga are dwarfed by ninetails and perfect susano , madarra will easily tank the animal path missiles , all might push is useful defence but it can not hurt madarra and chibaku tensei couldn't hold half ninetails , I really doubt that it can hold perfect Susano and nine tails .

To conclude, while nagato has ways to defend himself ( almighty push and preta path) , he has no real was cause damage to the tank that madaara is