I'm not a big fan of the basic Sig Sauer P365. I have handled one but have never shot one. Were I of a mind to go that route, it would be either my P365X or my M&P Shield Plus in the standard size configuration. This could change down the road but for now, that is my take on these guns. It is great that we have so many fine choices in this group of SD guns.
As for caliber, unless some unique situation forces me to go for a really small pocket gun, I will not carry anything less than a 9mm pistol. The .380ACP is at the bottom of the ladder in terms of effective SD use and I will avoid carrying a gun chambered for that cartridge unless I have no other choice.
I am looking for something for pocket carry - better than the 1st gen Ruger LCP I have. That is what the Glock 42 was supposed to do for me. I ended up giving that gun to my son. 98% reliable doesn't cut it for me.
The Sig 365 is a tiny bit more pocketable than the Shield Plus is. Not by much, but a little. I've read too many mixed things about the Ruger 380 Max. And, I won't even go there after the Glock 42 reliability issues. And, I don't want a SAO pocket gun with a thumb safety - so, that cuts out some other choices...
Comparing the Shield Plus to the 365, I prefer the Shield Plus too. But, I MIGHT buy a 365 for a specific reason. Not sure yet. I'm not 100% happy with the size (tiny bit bigger than I want). But, it was more pleasant to shoot than I thought it would be. I once had a Kahr PM9, and I hated shooting that gun. A lot of recoil because of the size. The 365 wasn't unpleasant to shoot.
I do prefer the trigger on the Shield Plus, though.
I plan to stick with 9mm most of the time. But for a pocket gun, I will make certain allowances. However, I will say that I was impressed with the Glock 42 for one thing. I could dump the entire mag in rapid fire, and shoot a group size that was much smaller with the 380 than I can with a mag dump on a 9mm. That was kinda cool.
Anyway, I am not really sure what I will do, because no one else makes a pocketable 380 that I want. The S&W Bodyguard is NOT what I want. The trigger sucks, and despite being a S&W product, the quality in that gun just isn't there. I watched several Youtube reviews on the gun, and many people pointed that out.