I've got a Sig P290 that's quite small, but its weight precludes pocket carry. It's a good 12 yds or less, defensive pistol, but is no easier to conceal, in reality, than my P229. Both have Sig's excellent night (read Tritium) sights...a must have for CC or night stand use, IMHO. And, BTW, I'm an OWB holster guy.
Just checked Sig's site: The 365 is an oz. heavier than my P290, with a bbl. that's 1/4" longer, it's roughly a 1/4" thicker and a 1/2" taller. For these add'l dimensions, it'll give you 4 add'l rounds (10 vs. 6), and a striker type trigger. I assume that means it'll have a shorter trigger pull and reset vs. the P290's which closely resembles a S&W J-frame revolver...ie. mucho long!
Overall, it's got a longer grip and that's the hardest dimension to hide for CC use...but you do get the trigger difference and capacity. For now, I'll pass.
Best Regards, Rod