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Rather than being rivals in strenght, I think those two have been rivals of attention and affections more, with Hashirama always being the winner. I mean, if their rivalry would have been about stenght only, then it shouldnt have been a blow to Madara that he didnt get chose to be Hokage, because we all know that even with EMS he still lost to Hashirama. I think the blow of not getting chosen by his own clansmen was far worse for him :/
And their rivalry extends to their family members as well, I know a lot of people have been dissing Tobirama for various reasons but from Madara's point of view, I guess Tobirama is mainly two things, 1) the living proof that he is inferior to Hashi, because unlike Hashi who still has a brother, he himself wasn't able to protect his own brother and 2) the man who killed his own brother. So uhm, even -IF- Tobirama would have been 180% different of character, even if he would have been all nice and pleasing, I doubt things would have been different much. Madara would have found other reasons to worry about regarding his clan, and they wouldnt listen to him, he would go mad etc etc.
Oh, and I guess he was jealous of Tobirama too because of the question he asked Hashirama ('who would you choose as your brother' etc).
So overall I think their rivalry was a healthy one, just that Madara's too sensitive, as he said so himself lol. The Uchihas dont seem to deal well with stress and tragedy :/