Rearrangement of a bicyclic dienone under acidic conditions
Your analysis of the possible products is excellent. I would consider both of the products to be major. Waring and coworkers studied this problem with a slightly different substrate (an extra methyl group at the 1-position, next to the carbonyl on the 'bottom' of the molecule). Under aqueous acidic conditions (sulfuric acid), the corresponding products were obtained in ~25% (mechanism A) and ~40% yield (product B). Only when run with sulfuric acid in acetic anhydride did mechanism B truly dominate (~90% vs 5% mechanism A).

There is actually a third pathway, where the methyl group shifts from ring juncture to ring juncture, and then goes through a mechanism similar to B. For the dienone in the question, the product is indistinguishable from mechanism B, but for the dienone studied in the publication, this gave another product in ~30% yield. I suspect that for the dienone in the question, the total yield of product B would be ~70%. That makes it appear as if mechanism B is dominant, but it is really two similar pathways operating that happen to give the same product.