They're both assholes. Shaq just has a more likable public persona because he often has amusing quotables. But, I think people knew for a long time he was an asshole too. Kobe's been an asshole since he entered the league. It's only in recent years that he's mellowed out and there are more people that actually kind of like him. The 2008 Olympics really helped his cause. Before then, players throughout the league didn't like Kobe. They thought he was a major head. A lot probably still do. But, LeBron and Carmelo especially formed a somewhat cordial friendship with Kobe from the Olympics.
But, both Shaq and Kobe were and still are assholes. And, it's both of their faults for their feud and for breaking up that Lakers squad, but Phil Jackson and Dr. Buss share in some blame as well. It's not an either or answer as to who was at fault. It's not a multiple choice: A, B, or C. It's D. All of the above.