No, Obito has Zetsu DNA, not Hashi DNA. Being Uchiha he should be able to handle the eyes no problem. Obito's problem was that he was using the six paths, while controlling tailed beasts, fighting 2 perfect Jins Guy and Kakashi. That is while fighting Madara's eye. And after becoming the Jyubi Jin, he had to also fight the Jyubi's power + the entire alliance while controlling the Rinnegan, and fighting for a few days straight. He's bound to have some problems doing all of that, while Nagato cucked it after a small battle.
Hashi DNA, shits on the entire Uzumaki clan. Hiq gates solod the 10 tails, restraining it completely, while Nagato almost died from 1 CT vs a 50% Kurama.