I have not owned a 391, so I can't do a direct comparison. I have owned a 390 for about 6 years. I have pushed it, used the heck out of it, modified it with barrel and stock and shot all three clay sports with it. Unbeatable. I would do it all again.
I prefer the 390. I just don't see the justification or need for the 391 unless you have really small hands. Even then, I don't really GRIP the forend of the gun. I just let it lie in my loosely opened palm and let my fingers just kind of touch the sides of the forend for comfort and support.
The 391 seems to have more problems in addition to being harder to clean. With the 390, you can "tune" the gas spring to suit the loads you are shooting. I don't think you can do this with the 391.
All the above info is correct according to Cole Gunsmithing.. The Beretta king.. He and other people make the parts to build either into what the factory should have done.. Buy gun.. add $350.00 parts.. Have a great gun..
The 390 in my opinion is much better than the 391 for several reasons. The gas system is much simpler to clean and the 390 receiver seems to hold up better than the 391's. And i too agree that the 303 is the best they have made.