The majority of women specific designs are designed around an average women's body. This body standard is smaller, lighter weight, and has a shorter torso and arms than the body standard of the average male that most non-women specific bikes are designed around.
If this average female body standard describes you, then you will most likely find a better a fit with a woman's specific design. Otherwise, if your build differs from this average women's body standard, a non-women's specific design may be a better choice.
For some women it simply boils down to size. There are a few companies now that offer extra small and extra extra small size frames, some are women's specific while others are not.
I usually try to support brands that offer a good selection of women's specific and/or women sized mountain bike designs. In addition, I support brands that offer both high end and low end women's specific or women sized designs. Check out the recommended brand sites for a selection of these brands.