The way that I understood the 3901 lineage:
The 391, as with all Beretta guns of the era, were being made in Italy. Beretta wanted to move on to the newer model (400), and discontinue the 391 from production. Meanwhile, Beretta had set up a factory in Accokeek MD to make the Army's version of the 92FS 9x19 pistol. The US corporate wonks in MD convinced the mothership in Italy to allow them to make the discontinued 391 domestically in the Maryland factory, relabeled as a 3901 (to differentiate it from the mothership's product) and produced with less costly finishes (matte blued, plastic furniture). The initial production runs were solely sold through WalMart, as best that I can remember, with a $599 pricetag. It proved to be a brilliant idea - Beretta sold the 400 as the 'nice' semiauto and the 3901 as the 'bargain' semiauto, without creating brand conflict and increasing sales / brand penetration in the process. As far as I understand things, all 390's will say 'Made In Italy' on them while the 3901 will all say 'Made In the US' on them, while being the same gun with cosmetic differences only.
Truth be told, I always fancied the 391/3901 more than the other Beretta gas guns. They were relatively simple and slim compared to later models, and had an amazing gas system that would reliably cycle anything from magnum duck loads all the way down to 7/8oz 1050fps target handloads equally well. The only reason that I sold my 390 and 3901's is because I fancied the Benelli M2 even mo'.