Markings are a study specialty for many FN/Browning collectors.
Since both guns were manufactured at the same factory, by FN I doubt that there was a diversion from FN to Browning markings. More likely, it was simply done as a cost saving measure since the BAC guns are sold in North America.
Remember the US considers the frame to be the 'heart' of a gun - the part without which a gun does not exist. Accordingly, the frame and not the barrel is required to be serial numbered. Other countries consider the barrel to be that part, and require it to be serial numbered.