First, they ask how this differs from the civilian trial of the Shoe Bomber, Richard Reid. Reid's attempted attack occurred in December 2001, before we had in place a military tribunal system, and before the prison at Guantanamo Bay had been established. The tactics and methods for fighting the nascent War on Terror were still being developed, and there really was no other option. Six months later, Jose Padilla, an American citizen, was detained as an unlawful enemy combatant, interrogated, and tried in the military system. The rules had changed.
Second, I am now hearing some ask about the 2006 civilian trial of Zaccarias Mossaoui, the "20th hijacker." This may be the single worst counter-example for Obama apologists to use. Mossaoui was arrested in August of 2001 - not only before the new rules I discussed above, but before 9-11. The failure to allow a search of his computer was identified as one of the chief problems that might have prevented those attacks. This is what began to shed a new light on the need to be able to apply military and intelligence rules in what otherwise would have been treated as domestic criminal investigations.
Further, Mossaoui was indicted in December of 2001, prior to Reid's attack. He made an absolute circus of pretrial motions and hearings, requiring multiple Appeals Court and Supreme Court rulings to protect national security before his trial was finally allowed to take place in 2006.
Mossaoui is probably the worst example these people could use to justify a civilian criminal prosecution of Umar Farouk Abdulmutallab, and not only because Mossaoui's arrest and prosecution began prior to 9-11.
In fact, the failure to connect the criminal and national security responsibilities in the initial investigation of Mossaoui led to changes in our approach to such investigations, and the five year circus of hearings and trials in civilian courts still stand as one of the chief arguments against that approach.
UPDATE: I should probably add, in case you are furiously trying to research some past terrorist whose case was mis-handled, that the most important point to make here is that two wrongs don't make a right. As I noted with regard to Mossaoui, his trial was a circus and it required the Supreme Court to protect the nation's security interests. You're supposed to learn from your mistakes, not justify bad decisions by pointing to the very mistakes you are repeating. Getting away from the law enforcement approach to terrorism was a correction. Giving Abdulmutallab Miranda Rights and a defense attorney is turning back the calendar to, well, to 9/10.