The problem with .32s and .380s is that as the guns get smaller, they are generally lighter as well. Most .380s that men pick out for women are of the Kel-Tec P3AT or Ruger LCP variety, this is not a very good option as they are so lightweight that the lesser caliber still results with more felt recoil. Even larger .380s are "blowback" operation (the barrel is fixed and does not tilt during the operational cycle) this also results in more fely recoil.
You best bet is probably going to be to find a mid-size metal framed 9mm before stepping down to the .380 and .32 as the gun will have characteristics that will make for a more friendly shooting experience.
Now back to the question, I would take a .380 over a .32 any day of the week. "Stopping Power" is a very subjective topic. All handguns of general service caliber and below are poor man stoppers. The .380 is generally thought to be the lowest caliber in an auto for carry.
This is part of a study done by Greg Ellifritz of the Tactical Defense Institute covering 10 years of shootings, while this information is not intended to be the end all/be all of the caliber debate (wouldn't it be nice if there was one?) it's a decent reference off of real world data including single shots and multiple shots.
The rest of the article can be viewed HERE