I have a Bersa Thunder 380 as well as a Sig 365.
The Bersa is blowback, and even though it is a little heavy, the recoil is stout because of the blowback operation. I can shoot it fine, but me wife does not like it. Follow up shots are slower. It is quite compact however, but not nearly as compact is the 365. I know you said 380, but hear me out. I am only comparing the Bersa to the Sig here.
Here are some of the my takeaways for CC use:
Bersa specs:
500g without mag, 168mm long
Single stack 380
Rear sight adjustable with screwdriver, with bright dots
SA/DA hammer with double strike and safety
You can buy wood grips for it, or laser grips
P365 specs:
465g without mag, 146mm long
Double stack 9mm
Tritium sights standard
Consistent trigger pull striker action
You can buy a laser or light for it
Pros for each gun (rather than listing pros/cons) :
P365 has a better finish and is less likely to rust
P365 is lighter and about 1" shorter than the Bersa, about the same height
P365 is more narrow due to lack of safety control
P365 you can use the mag release without shifting your grip (Bersa is 1cm away from thumb)
P365 is less expensive to train with
P365 is much easier to field strip
P365 you can buy a threaded barrel
P365 is much less likely to snag on something when being removed from a purse
P365 probably has a better warranty (I got my Bersa used, no warranty)
P365 holds a few more rounds even though it is smaller (I short the mag to keep the weight down)
P365 is easier to rack the slide because of more grip surface and there is no slide mounted safety digging into your hand
P365 is much easier to load a mag under stress due to the shape and size of the mag and magwell
Recoil is similar between both guns, maybe less on the P365
Both guns offer extended and flush mags
Both guns are accurate and equally reliable with good ammo
Bersa has a safety (if that is what you want) with decocker
Bersa sights I would say are better during daylight or in a well lit area (but not direct sunlight)
Bersa has a slightly more comfortable grip for me, but less comfortable recoil (blowback + bore axis)
Bersa mag disconnect can be easily removed
Bersa has a trigger lock (you could also call this a con)
Bersa has nickel and gold finish controls that can be purchased
Bersa design is more simple and easier to fix yourself
Bersa parts are less expensive
Bersa is easier to rack the slide if you pull the hammer first, but the safety still digs
Bersa slide release is larger and much easier to drop the slide
and the big one..
Bersa is half the cost of a P365... but if you do take it to the range often, it costs more to shoot.
After 1800 rounds the 365 is less expensive to own, and if you are considering other guns in 9mm, you can stick to a single caliber. 9mm is also obviously more terminally effective than 380, especially through heavy clothing.
If I used a purse, the Bersa has a large beavertail and a hammer which can snag. If I carry on person, the Bersa is longer and fatter and heavier and more likely to rust if you get sweat on it. Sig wins for both these scenarios. They do make a CC version of the Bersa Thunder, but it is even less comfortable to hold and shoot.
All that being said, if neither of those are a concern, both my wife and I prefer something like the P07, it is easier to grip, holds more rounds, cheaper mags, better trigger, real rail, easier to rack the slide, less recoil, more fun to shoot.
Other guns... I did NOT enjoy shooting the Glock in 380, the Walther PK380 is not even close to reliable, I think I shot a Shield and did not like that either, and those are the only other 380 I have shot in recent memory.