From what I just read it should be the other way around. They should be marketing anti-perspirants to men saying that they are good enough for a woman to use.
A woman's armpits are smellier. Men perspire most heavily on the upper chest, from eccrine glands that secrete mostly salts and water. Women perspire most heavily under the arms, from apocine glands that secrete milky substances along with salts and water. Bacteria digest the milky substances, and their by-products make this sweat smelly.