I REALLY wanted to like the P365. Then I shot one (the XL version). For some reason, it consistently shot about 3" low for me at about 10 feet. It didn't do that for the gun's owner, so I figure it's something with the way I was gripping it, or something. It was really odd. I'm a decent pistol shot and took my time, focusing on the fundamentals.
My buddy's Hellcat shoots much more to point of aim for me.
Point being, try to get a little trigger time with one before you buy, if you can.
I've shot the hellcat too. Plastic and strikers aren't my thing, but that its grip felt good in my hand. I don't have large hands so I'm not a double stack mag lover either, but it seemed to have a bottomless magazine - i dont recall the capacity but it is surely enough to ward off any injun attacks!
I had a chance to handle and fire the 365 and 365XL side by side, and sadly for me, neither did it for me. Which really sucked, as I really, really wanted to like the XL. The standard 365 was just flat out too small for me. Good trigger and sights, just too small. The XL had a funny grip angle similar to the 320, that just felt "off" for me. And, for me, the flat faced trigger on such a small gun was quite uncomfortable for me. Both triggers broke as expected and reliably, just that neither worked for me as I had expected and wanted them to.