Actually, if I understand the rulings in
Hamdi v. Rumsfeld and
Hamdan v. Rumsfeld (which relies on Hamdi), basically, the US Constitution through the Due Process Clause of the 14th Amendment guarantees US Citizens the right to the writ of
habeas corpus to petition the federal courts to review the basis of, and question/fight against, an executive detention (unless habeas corpus has been suspended by Congress), also to have the court determine their status as a civilian (wherein civilian law would and courts would prevail), a lawful combatant (where the UCMJ and the Geneva and Hague Conventions would prevail), or an unlawful combatant (where the UCMJ would prevail but without the protections of the Geneva or Hague Conventions), it further guarantees the right to council, and ensures the right to access to the federal courts. However, they do not specify which courts a detainee, US Citizen or not, must have their case heard by and within. Military tribunals are a Federal Court. The US Code defines what an Unlawful Combatant is, and a terrorist meets that definition, and allows for them to be tried in a military court.
I think that it matters more where the person was caught, and whether they enter the federal court system via civilian authorities or military authorities as to which court system they may end up having access to for habeas corpus and beyond.
http://www.americanbar.org/content/dam/aba/publications/individual_rights/hamdi_v_rumsfeld.authcheckdam.pdf