Read Gareth Porter's analysis of the causes of animosity between the two.
I didn't know about any of this last night but I found it interesting how Petraeus brushed off Jim Lehrer's question about "who is your boss?" He responded with:
"Admiral Fallon, the Central Command commander, of course up to the secretary of defense. But, in fact, the counterinsurgency manual, what it calls this is unity of effort. It's not unity of command. There's not one of us that's in charge of the other, but there has to be unity of effort."Thanks Nunya for the tip!
Trivia: Did you know that in 1987, Petraeus completed a PhD thesis (in the Wilson Woodrow Center) entitled "The American Military and the Lessons of Vietnam", examining the influence of the Vietnam War on military thinking regarding the use of force.
Here's a PDF version of his thesis.
Judging from the abstract, the General to become, seems to have been too sad that Vietnam had made the military too cautious to use force all the time and he seems to have suggested the post-Vietnam cautiousness to have been a pitfall!