I think the fulcrum in all the tensions and problems Michael had with Roth were Fredo. Fredo resented being "passed over" as he saw it. Now whether he "ran into Johnny Ola" and got used and manipulated or actually sought out Roth/Ola and suggested certain things, it's Fredo's issues which allow Roth to make his move.

But would Fredo have had those issues if he was firmly under big brother's Sonny's thumb in NY? I'm not so sure. Sonny would not have been able to see the big picture like Roth or Michael, but on the other hand with Sonny in Pentangeli's position Roth would have had no belief that he could make an attempt on Michael's life and in the case of failure try to blame Sonny. Michael held back on settling accounts with the Rosatos to close financial deals with Roth and find out who set him up. Would Michael have been so blase about this chess game if it were Sonny's life at stake as opposed to Pentangeli's? Well the Michael by the end of GF2 would be sure. But earlier?

With Sonny around with his famed temper and unquestioned loyalty I think Roth would have had to find a different approach to deal with Michael. And I wonder if the Rosatos would have even had the stones to challenge Sonny, as opposed to Pentangeli. Either way I don't see Sonny asking permission to war with the Rosatos. He would have come out blasting. Of course it's Sonny so maybe he still makes a fatal mistake in a barbershop or club somewhere...

But I think the Michael:Sonny or even the Sonny:Fredo links were much much stronger than the Michael:Fredo relationship. And maybe Sonny, as opposed to Michael, keeps Tom around, which would likely make both Tom and Michael much less stressed..