In political terms, the right likes the war idea because it involves taking terrorism more "seriously." But in doing so, you partake of way too much of the terrorists' narrative about themselves. It's their conceit, after all, that blowing up a bomb in a train station and killing a few hundred random commuters is an act of war. And war is a socially sanctioned form of activity, generally held to be a legally and morally acceptable framework in which to kill people. What we want to say, however, is that this sporadic commuter-killing isn't a kind of war, it's an act of murder. To be sure, not an ordinary murder--a mass murder--but nonetheless murder. It's true that if al-Qaeda were something like the "blowing up train stations" arm of a major country with which we were otherwise at war, it might make the most sense to think of al-Qaeda as fitting in with spies and saboteurs; criminal adjuncts to a warrior enterprise.
After all, do we really want to send the message to the world that a self-starting spree killer like Nidal Malik Hasan is actually engaged in some kind of act of holy war? It seems to me that we don't. A lot of people in the world are interested in glory, and willing to take serious risks with their lives for its sake. Insofar as possible, we want to drain anti-American violence of the aura of glory. And that means by-and-large treating its perpetrators like criminals.
I particularly like the point about how the "war not crime" frame actually buys into the the narrative of Al'Qaeda. I think there' also something to be said about what war does for national identity. The notion of supporting our troops as the make the world safe for democracy gives you a kind of missionary edge that simply protecting the citizenry from murderous thugs (international murderous thugs, to be sure) doesn't. The latter is a duty that any second-tier nation must try to before, the former is the business of paladins. The "war not crime" narrative is a natural extension of the "America can do anything" narrative.