Well since Nagato has both Rinnegans, Obito can't have any either way. Nagato and Konan knew how Obito's Kamui worked which is how Konan did more damage than Kakashi, Naruto, Sakura, Sai, Yamato, Hinata, Kiba, and Shino combined could do when they first fought Obito. Nagato is a sensor and have stronger eyes than Obito so I don't see Obito getting a surprise attack on him. If someone wants to use DMS Obito then I'll use Prime Nagato who is much stronger and faster than weakened Nagato. Nagato's precision with BT is so skilled that he pulled a needle out of a plank of wood; imagine him pulling Obito's eyes out their socket the moment Obito is tangible.
Obito can try but Nagato being a sensor and having the Rinnegan would ensure that Obito's attempt at that fails.
Obito would only be fast at Kamui-ing his own body, if Nagato was in his prime he would beat DMS Obito so if you want to use a stronger version than so would I. Nagato uses his summons to have shared vision, is a sensor, and can use Deva path to stop all of Obito's attacks. If Nagato gets his hands on Obito l, he'll rip out his soul; if Obito takes them both to Kamui dimension before this then Nagato insert Obito's eye and Kamui out. Nagato can also use his bird summon to fly out of Obito's range. Obito doesn't have Sage chakra, he had it as the JJ and only had it afterwards after he absorbed some from JJ Madara; it gets used up and is gone; that's like me saying Nagato has a ton of chakra that Edo Nagato absorbed from Bee.
Either Nagato has a strategy to attack Obito continually for over 5 mins to kill Obito or cause him to use Izanagi (which leaves Obito with 1 eye) or they keep countering each other until one runs out of chakra or becomes fatigue. But Nagato can absorb Obito's ninjutsus so he can regain his stamina in that instance but I'm sure Nagato has a larger reserve than Obito.
