This piece in Politico hits the major points:
The defense secretary, regardless of his lofty title, was never part of the president’s inner decision-making circle on foreign policy, which the sources said would remain intact (and it’s worth noting, the sources said, that powerful Joint Chiefs Chairman Martin Dempsey is), and few expect his departure to solve the deeper problems plaguing Obama’s national security team given the iron grip exerted on foreign policymaking by Obama’s West Wing staff.
And the move alone will do little to help a struggling second-term president mend what the sources said were far deeper rifts within his overburdened West Wing-based national security team, pointing in particular to long-simmering tensions between McDonough, who had been deputy national security adviser before moving up to chief of staff, and Rice, the worst-kept secret struggle in Washington.
More broadly, the dumping of Hagel leaves unanswered the key foreign policy dilemma that hangs over the remainder of Obama’s presidency: It’s clear that Obama, propelled to office six years ago on the promise of ending two unpopular wars, must now radically readjust his priorities from a posture of military withdrawal and Pentagon budget cuts to one of engagement, but it’s not at all clear how he plans to do so.
Hagel’s main gripe, according to people close to him, was what he viewed as a disorganized National Security Council run by Rice—a criticism shared by McDonough, according to a senior administration official. (An email to McDonough wasn’t returned.)
That observation puts Hagel in good company: His predecessors as defense secretary, Bob Gates and Leon Panetta, have both taken the unusual step of publicly criticizing Obama’s White House team for power-hoarding and dysfunctional decision-making at the expense of the Pentagon. “The whole system is dysfunctional. The lines of communications [between the NSC and the Department of Defense] are totally broken,” the staffer told me. “I hope that whoever takes over fixes it, and fast.”
*Yeah, yeah, I know this wasn't planned. I'm talking about effect, not intent. And I'm not dismissing the importance of the news from Missouri, either.