First, we should discuss some physics terms:
Momentum = Mass (of the bullet) x Velocity
Jerk = Mass x acceleration of the Acceleration (or the derivative of acceleration velocity)(in a car.. when your head rally snaps back when your friend burns rubber)
Higher order effects include the shape of the acceleration curve
So the same momentum transfer might be felt by a big cuddly bear hug (heavy and slow) as lighting off a .454 Casull (light and fast).
Then there are old fashioned rubber shotgun pads that spread out the impulse (the shape of the momentum transfer) but absorb very little energy by converting the recoil to heat… and isomer pads that technically do absorb the mechanical energy and turn it into heat.
What we feel as recoil will depend on the amount of momentum transferred, the shape of the transfer over time (lighter and faster, like .357 Max may feel “snappy” or “slappy” while big bore revolvers with slow but heavy bullets, resulting in the same momentum, feel “pushy”), mass of the pistol held in hand, how well the grip fits the hand, the bore axis of the pistol (push vs twist), and the method of cycling the action.
The same semi-auto gun with the action welded shut will have more perceived recoil than if the action is free to cycle, slowing the impulse to the hand in the shape over time of the event.
So, .380 vs 9mm… we have to ask “for what ammunition”? Buffalo Bore .380 might push the same bullet faster than a 9mm plinking load. (You can buy such stuff.)
Then you need to know the weight of the guns. My Bersa Thunder is fairly stout, but not as heavy as some of the all steel .380s of the WWI / ww2 era.. and some of the little pocket 9mms are way too light for me to want to fire off!
My Bersa uses a blowback design, while most all 9 mms and most .380s use a moving barrel design.
The easiest answer is, the smaller the pistol, the more it kicks.
The S&W .380 EZ is not a pocket pistol. It’s got some heft. It’s got a good action and has very manageable recoil. The same gun, chambered in the average 9mm ammo, will kick more.
A CZ 75 SP-01 weighs 41 oz (2.6 pounds) will kick less.
If recoil is a big concern, the S&W .380EZ is widely admired as a serious pistol. It’s large enough to provide good grips, heavy enough to control recoil, not a blowback operation so more perceived recoil is absorbed, yet small and light enough for easy carry. Especially with modern ammo, .380 is no joke. Someone will pipe up that they think it’s wimpy and only 9mm will work. I challenge such a man to let their angry girlfriend shoot them with a .380 as a YouTube challenge. They will be sent to the same hospital or morgue as if they were shot with a 9mm, depending on how good a shot the woman is in either case. Disclaimer: don’t shoot people with guns, it will kill them.
Personally, I love the inexpensive and excellent Bersa Thunder. It’s a bit bigger, heavier, and the blowback operation is super simple and reliable although it takes some minor experience and hand strength.