Is obito Uchiha and Madara Uchiha the same person?

Now to simplify things, no, Madara Uchiha and Obito Uchiha (tobi) are not the same people. Madara saved obito from death, obito took the name of tobi and later acted as if he was madara for the real Madaras plans.

Who is stronger Madara Uchiha or Obito?

9 Stands No Chance Against: Madara Uchiha After Sasuke, Madara is undoubtedly the strongest known Uchiha in the history of the series. ... Madara was much stronger than Obito to begin with, and the fact that his version of the Ten-tails was perfect made him even stronger.

Why did Obito claim to be Madara?

Madara took in Obito. He was already very old and could not live much longer. So he wanted Obito to find someone to whom Madara can donate his newly obtained 'Rinnegan' (which is Nagato/Pain) to use reincarnation jutsu on him(Madara).