Noticeably less energy use, small difference in damage... and I believe it has a faster speed or some other miscellaneous attribute that I found desirable. Maybe a faster fire rate.
As a side note, a Reshep can fire two Basic missile turrets at a time, but not two Order missile turrets.
I originally had a dual missile loadout, a while back. Perhaps I could stand to switch back to Order missiles - but again, they use more energy and are slower, I believe.