The 390 case is about 10mm longer than the 380 case, otherwise diameter is the same.
The Over All Ratio of the 5:1 boxes is 45.66:1 as compared to the OAR of 3:1 of 39.33:1 and 4:1 of 89.14:1....all of the Taigen variety (from my tooth counting so beware.....lol)
The 360 motors do not have the torque of the 380's nor of course of the 390's if all else is equal.
I'm happy with my 5:1 boxes which both reside in StugIII tanks since they lie really flat to miss the low profile of the Stug interiors, so I can see why they work well in the Panzer III. Don't expect large amounts of torque though, and putting them in a large Tiger 1 is questionable. My Tiger 1 has steel 4:1 boxes, with 390 motors, and it needs it with the weight of all those large diameter wheels and sprockets, not including the wide and dense tracks with mondo traction. I doubt 390's will fit end to end in the Tiger with the 5:1 boxes, since the endbells align directly only in these boxes.
Perhaps someone has an extra pair of 4:1 boxes they would trade you for??
Jerry Rude