I don't know if Barzini was "loved" but he was certainly respected. In the movie, you see Tattaglia looking to Barzini to direct his actions during the commission summit conference from which Vito concludes "it was Barzini all along."

As for other discussions in this thread about the comparison of Michael to Vito, I think a part of the difference is cultural. Vito understood from his heritage that being a "Godfather" really did mean acting like the patriarch of a very extended family. You can see it in the way Vito Corleone is so solicitous of even the most humble of people -- like the baker who is worried about Enzo.It would seem Don Tomassino was cut from the same cloth. It was not only about making money and killing people, it was about making sure "his people" were cared for and got chances in life. He built his whole empire by doing favors for people and then making them promise to return the favor another day. Michael, on the other hand, is more in the American tradition. Not as religious as his father, he saw the position of "Godfather" as something that simply came with the territory. He ran things more like a CEO than a patriarch.