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Why? if read below the bolded part you can read why i think so. Or is something in it unclear?
But I see where you're coming from. And understand that this is all hypothetical. There is no supporting evidence because its made up. Obito did die so we will never truly know what happend if he lived.
What I want to know from you is how does Tobi intent to control Kurama without the sharingan? And if you agree he cant why would he release him?
Obito might have joined akatsuki and spy for konoha , he could have warped away uchiha shisui's eyes and protecting them and use them when necessary like against orochimaru or tobi , he could have formed a new uchiha sanin team which consist of himself , itachi and shisui, he could have been the taijutsu expert while itachi was the ninjutsu and shisui , the genjutsu expert in the team ... he could have been the best prankster to ever live ... just imagine warping kakashi while he is sleeping and he finds himself in the middle of nowhere , or he could have been the biggest pervert , slipping through the girls bath house xD and maybe rin could still have been alive
Tobi has shown an extensive knowledge into jutsus, events, and people. After all, he did confess to having many "doors are open to him" 
If Obito's eyes are not available, then I am sure Tobi will find another way, or another dead Uchiha in the battlefield.
Like I said, Minato's death is not connected to Obito's. Tobi wouldn't have wasted the chance to unleash the Kyuubi and blame the Uchiha.
at the start of the series, in the entire history of the uchiha clan, only 3 people unlocked it, madara, izuna and itachi
i highly doubt obito would have unlocked his MS, so his survival would not have directly changed anything from his interference
Also, obito would probably have died in the uchiha massacre. itachi was good enough to kil even the veteran ninjas.
The mian influence would probably come from the fact that tobi wouldn't get his eye.
It's arguable though, because if tobi was so powerful, he probably could just kill obito in an instant with his other sharingans and their MS skills and take his eye. this must then be balanced against the fact that tobi might not even know what obito's eye does so he might not even go after him in the first place.
Kakashi would have less regrets, but Obito would probably be dead, and Kakashi wouldn't have the Sharingan. He has shown nothing special that would make him strong with Sharingan.
tobi is not obito,that's sure.in fact, he fought minato some years later claiming he had been waiting so long for kushina's pregnancy.also,his face is identical to the one kisame recognized as madara. I doubt obito could control someone like the 4th mizukage yagura. yet,even if he had survived,that'd be meaningless...
i've read a lot of people saying obito would have turned out less talented than itachi/sasuke/shisui/etc because he was but an average shinobi at the time of his death...let's not forget that naruto also was at the very bottom of his class,now look at the guy.
now,putting in perspective of the way kakashi and gai competes...and kakashi plays along...i would have to say that he would not have passed the chance to spar alot with his fellow team mate(an uchiha at that).
so, i imagine if obito were to live...him and kakashi would have driven each other to be strong.
but,let's take into account that rin was the driving force to awaken his sharingan...so the rin kidnapping would have to happen...
otherwise,he may have stayed a slouch for a good little while.....