I do have to wonder if there was some personal element in Barzini's seemingly obsessive desire to destroy the Corleones? Yes, he'd become much more powerful with them out of the way. But at what cost? At what risk? The urgency of his actions, and the rapidity of it all, makes his actions seem almost personal rather than business. Barzini's moves were calculated but they were very rushed. Contrast that to the Corleone plan. The Corleone's wiping out of the rival Dons was much less subtle, but also much longer in the making, more thought out and ultimately more effective.

Barzini was taking on a lot of risks and making a lot of assumptions. That Sol would be an obedient puppet and not simply align himself solely with the Tattaglias. That Tattaglia would be willing to be the front-line combatant in what could be a long and devastating war with the Corleones. That Vito would let his guard slip. That Sonny would be a hothead.

He was playing a chess game, but he seemed to be rushing through it rather than taking his time and playing out the possible scenarios. Again contrast that with the Corleones - they took a calculated risk - made themselves purposely weaker - so that they'd be less expected to strike, and when they did, it made them that even more powerful than Barzini could've dreamed of being. Michael could easily install four other puppet Bosses, absorb the drug business, and win back all of the Corleone's lost business and territory.

Where Barzini's end game was to simply take Vito's place at the head of the table, Vito/Michael's was to not only head the table, but choose who sat at it as well.

I think that Barzini was opportunistic, so timing was something he couldn't control. Chances are that the end of the war the catalyst - like legitimate businesses that had to cross the ocean, Sollozzo's operation was probably handicapped during the war. They'd have to get up and running quickly to keep others from taking the business.

Woltz, as I posted elsewhere, Vito didn't realize until after the Dons' meeting that it was Barzini all along. Sollozzo was a tool for Barzini to use to replace Vito at the apogee of the NY underworld. The drug traffic could have survived without Vito's (or Sonny's) help and, backed by Barzini, it would provide considerable income to Barzini. So, to the extent that any machinations in the underworld are personal and not business, then, yes, Barzini's efforts were personal.

I think Barzini's moves against Vito were "personal" in the sense that he thought of himself as No.1 waiting in the wings, impatient to be the top dog in NYC, younger than the other Dons, whom he regarded as "Moustache Petes" (per the novel). But, I don't think he had a personal grudge against Vito.

I also don't think he was in a big hurry. He waited until after Vito died to make his move against Michael. That was years after he and Vito "made the peace" after Sonny died.

The beef between Vito Genovese (represented by Don Barzini) and Frank Costello (represented by Don Vito) almost perfectly emulates a real life story.

I believe Barzini was all about entitlement. Not one to wait in teh wings to inherit a throne, he sought to take it by subterfuge.

Barzini was slipping!
I reckon he got taken in by Corleones strategy - weak, forced to leave New York - that Vito had no sons to take over
Nobody was expecting Michael to take over or effective as Don if he did He agreed to meet Barzini in Tessio's territory

Civilian personally murdered Sollozzo and New York Police captain I reckon the hostile looks they exchanged at Vito's funeral should have tipped him off