People seem to be getting off topic, as such I will contribute to all points I see, off topic and on topic.
1st (On-topic): I will assume that being the original developer on the Rinnegan, Madara would presumably have access to jutsu's that Nagato may have been unaware of. People need to remember that almost of the the Rinnegan abilities Nagato knew who taught to him by Obito, who learned them from Madara. What's that old say: "I taught you everything you know, but not everything I know."
Another possibility is that with access to Hashirama and Sage mode energy that Madara's Rinnegans "push ability" became more focused and with the ability to pin-point targets more flawlessly. There is really no way of knowing which two scenarios are correct, could even be both.
Now to discuss the off-topic debates I see going around;
There is absolutely no way to compare Madara and Nagato as far as who was more powerful and whom wielded the Rinnegan more proficiently and I will explain why,
Pain/Nagato: I would hope we could all agree that Nagato as pain was far from the true abilities of Nagato. First off, Nagato as Pain from the get go was a weaken status. Controlling 5 individual bodies, because you're incapable of moving on your own, while each performs different jutsu's is not an easy feat. This wasn't done because Nagato felt it would be more efficient, he really did not have a choice, and considering all this chakra was divided between the 5, its no wonder it was only a matter of time before he was beaten by Naruto. As for why he couldn't capture Kurama, it has already been proven that a bijuu in a human body is stronger than a Bijuu going on its own. Therefore, Kurama was already stronger than when Madara subdued him, and when he finally decided to capture him using the bolder jutsu thing, he was already running on fumes, given his facial expressions. In closing for Pain/Nagato, it was sent to capture Naruto, not kill him. Therefore it can be concluded that he didn't go into the fight with the mindset of going all out. He fought with a level of discretion.
Edo Nagato: As an Edo, with all the rinnegan in one body, Nagato was more than capable of dealing with Naruto and Killerbee with relative ease. We also know that Edo forms are far less powerful than their living counterparts, Madara being proof of this. So a less than 100% Nagato was too much for Naruto and Bee, while at the same time Nagato was unable to move on his own. So essentially, he was owning them while handicapped.
Nagato solo/living: We have no clue what a living, uncrippled Nagato is capable of.... That is just the truth.
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Madara during his own time: Pretty a no contest, Madara before his defeat by Hashirama has no way of dealing with a Rinnegan, imo
Madara after awakening the Rinnegan: Old age, surviving by being attached to the tree, not sure there is a contest.. not sure we should even count this one due to age. not a fair comparison
Edo Madara: Thiis Madara is far less powerful than when Madara is revived, however, this Madara is not completely Madara. This Madara has had his abilities almost doubled by fusing Hashirama's DNA into his own... So I dont see this being a fair comparison either given the outside interference. Might just be me.
Revived Madara: Far more powerful than Edo Madara as proven by the manga, but with the same interference of having Hashiramas DNA. Not only that but Revived Madara also stole Sage Mode from Hashirama as well, Which I'm sure increased his powers by 1/3 at least. So this one should not count either.
Revived Madara, without the stolen abilities: We have no idea what his form of Madara, but we can assume him to be at least 2 and 1/3 weaker than the Madara we see now.
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So no one side can say that either is stronger than the other, given the handicaps on both sides.
Just my thoughts. Sorry for any grammar errors, I did this while at work and switching between screen.