We saw enough of Barzini at the Commission meeting to get a feel for his style. He was clearly younger, more modern, and ready to step into a leadership role, than the other Dons. One of my astute GF-watching buddies noted that Barz is the only Don smoking a cigarette, not a cigar. I wasn't that interested in the rest of them.
I once thought about an alternate denouement for Barzini and Michael: Barzini asks for a private sit-down with Michael and Vito. He congratulates Michael on his position, then tells them that Moe Green talked to him about the future of his hotel. Barzini notes that he knows the Corleones have a big stake in the hotel, and he wanted them to know about that contact that was taken behind their backs. From that opening, perhaps Barz and Michael might have struck a deal to get rid of Moe and put their own, mutually agreed-upon front man in charge of the hotel.
I don't think the cigarette is as visually important as the fact that he's the only Don involved in the war who doesn't have a moustache. Vito and Philip Tattaglia do.
He might've been younger and more astute, but he overplayed his hand by making clear it was he who was behind the War all along by being so insistent about the drug trade. Basically gave himself away in much the same fashion as Sonny gave away his interest in the drug trade which led to Vito being shot. What Barzini had in youth and ambition, Vito had in experience and quiet listening--Which is what led him to quickly determine that Barzini was behind it all along. Vito probably had suspicions about Barzini having some part (given Vito saying that Tattaglia could have never outfought Santino), but Barzini's own words made it so that there was no doubt.
Had he listened instead of talked, he might never have given away that HE moreso than anyone was interested in the drug trade, and thus gave away that he was the mastermind behind the war, and he might not have been targeted by Vito/Michael in their vengeance.
And with regards to your alternate ending, I don't see Vito/Michael putting aside the fact that Barzini was behind the war and had Sonny killed. I don't see them entering into a partnership with a party whose aim was to destroy the Corleones.
