.380 is and remains popular in the US. But we don't see that up here as most of the guns chambered for .380 are smaller and thus in our Prohibited category so they don't get imported.
To set the stage a little more when I lived in Burnaby I helped out now and then for Ladies night at DVC. So I got to see a lot of low and first time girls shooting handguns. I quickly found that there are three things that really affect them that are not significant for most guys.
First off is that if they can be sensitive to hard recoil and the loudness of the report. They typically get past that pretty quickly.... unless someone sets off a .500S&W in the lane next to them...

But if they don't then they tend to be nervous and flinch a lot. I've seen a few of those come back to shoot in quieter times and with less noise around them they did a lot better. They'll get used to it but if the noise and recoil bothers them at first it might take a few sessions to get past it. It seems like stobrien's wife is at that point where .22 is fine but the 9 has a bit too much kick to be comfortable with shooting.
The smaller and slighter ladies often don't have the muscle development to hold a handgun out at arm's length for the time it takes for a full magazine. Part of this is the relative size and weight of the gun and part of it is that if they are smaller than average then consider that for them it's like a regular guy holding out a Desert Eagle for a full magazine. So in such cases we need to cut them a bit of slack and understand that they might want to take a break. It's not that they CAN'T hold the gun long enough. But that their muscles will lose the steadiness needed for accurate shooting. There's no shame in clicking on the safety and lowering the gun to the bench and resting one's arms.
Finally if we expect our ladies to shoot well we need to fit the gun to their hand sizes. A small hand might be physically able to hold a Beretta 92 or an old Gen 3 Glock but they don't fit well and allow them to have a proper amount of finger wrap around and support the gun correctly positioned in their grip. So the deck is stacked against them being able to shoot such a gun well.
The full size 9mm guns that I found fit in small hands well and which are more commonly available were single stack 1911's, Ruger SR9, CZ75 (Stock grip is OK but it's better with the thin aluminium grip scales) and the S&W M&P with the smaller grip back. In the case of the CZ it's got a pretty fat grip area but the thing that makes it fit small hands well is the egg like cross section to the grip with the point of the egg shaped cross section running along the back strap. Being narrow and roughly the same shape as a 1911 along the backstrap is what seems to make it work.
Take this for what you wish but it's what I observed and the feedback from the ladies that tried a bunch of different guns over a number of visits that is the basis for what is in this post. It also matches what I heard from the girls we had working there as RO's.