The military charters can be on any equipment. Equipment is sized to the need. The NBA charters are all flown on a 757 subfleet with all business seating and more room than normal business. The NBA owns the aircraft and Delta manages and staffs them.
Seating on military charters is up to each organization however as a general rule the loading crew gets to sit in front. Remaining big seats seem to go to officers on army and air force charters. Marine Corps charters seem to always put officers in back and NCO’s in the front. Even the Commanding Officer is usually in back.