If this man has broken laws of the United States and is within our jurisdiction, then we as a country have a moral obligation to prosecute him in federal court, for all eyes to see. To do so under a military tribunal means that no one will see what goes on.
Terrorists think they are more than just mere criminals. They are not. They should be treated the same way any murderer or rapists would be treated. So, Sulaiman Abu Ghaith should be tried and convicted in a federal court. It should not be and nor should it ever be a military tribunal.
The only evidence that the government has on Abu Ghaith is that he was a spokesperson for Bin Laden and Al Qaeda. There is no support that he participated in attacks or was guilty of murder or terrorism. All that we know is that he was a voice for his family.
This isn't support for Al-Qaeda. However, what federal crimes is Abu Ghaith accused of? The federal courts have jurisdiction over the United States, but if Ghaith operated overseas, then the crimes were committed in a foreign jurisdiction and should be handled by the local government. Unless the US thinks it has jurisdiction over the world, then no he shouldn't be prosecuted.