The major differences are summarized here. There are differences in process, in who serves on the jury, and... most importantly - in punishment.

For example, UCMJ Art. 134 says this:

Though not specifically mentioned in this chapter, all disorders and neglects to the prejudice of good order and discipline in the armed forces, all conduct of a nature to bring discredit upon the armed forces, and crimes and offenses not capital, of which persons subject to this chapter may be guilty, shall be taken cognizance of by a general, special, or summary court-martial, according to the nature and degree of the offense, and shall be punished at the discretion of that court. As used in the preceding sentence, the term “crimes and offenses not capital” includes any conduct engaged in outside the United States, as defined in section 5 of title 18, that would constitute a crime or offense not capital if the conduct had been engaged in within the special maritime and territorial jurisdiction of the United States, as defined in section 7 of title 18.

That in addition to the fact that the criminal conviction would affect benefits (but I believe that may be true regardless of the jurisdiction).

Also worth highlighting that charges in a military court are brought by military personnel, which Trump may think could be ordered to do so while the DOJ (supposedly...) cannot.

There's also the political question: Trump has repeatedly and consistently been trying to insert the military into the civilian political discourse. This is just another attempt at this.

The major differences are summarized here. There are differences in process, in who serves on the jury, and... most importantly - in punishment.

For example, UCMJ Art. 134 says this:

Though not specifically mentioned in this chapter, all disorders and neglects to the prejudice of good order and discipline in the armed forces, all conduct of a nature to bring discredit upon the armed forces, and crimes and offenses not capital, of which persons subject to this chapter may be guilty, shall be taken cognizance of by a general, special, or summary court-martial, according to the nature and degree of the offense, and shall be punished at the discretion of that court. As used in the preceding sentence, the term “crimes and offenses not capital” includes any conduct engaged in outside the United States, as defined in section 5 of title 18, that would constitute a crime or offense not capital if the conduct had been engaged in within the special maritime and territorial jurisdiction of the United States, as defined in section 7 of title 18.

That in addition to the fact that the criminal conviction would affect benefits (but I believe that may be true regardless of the jurisdiction).

Also worth highlighting that charges in a military court are brought by military personnel, which Trump may think could be ordered to do so while the DOJ (supposedly...) cannot.

There's also the political point: Trump has repeatedly and consistently been trying to insert the military into the civilian political discourse. This is just another attempt at this.