Just got my p365 and so far I am impressed. It is not a perfect pistol, but it is a distinct improvement over my PM9. Aside from the extra capacity, the biggest difference is how fast I can put a follow-up shot on target. I broke out some graphing paper and compared the two: the barrel on the p365 definitely sits a bit farther down - closer to your hands.
The picture kind of washed out when uploading, but the p365 barrel is about 1/3 of a graphing square lower than the pm9. There are 4 lines per inch, so thats about ~1/12" difference. Doesn't sound like much, but you really feel it.
Sig's fit and finish is better than the PM9. I've always hated the PM9's air gap between the front of the slide and the frame and how the front of the slide nose-dives when dry firing (makes it harder to verify I'm not flinching). Plus the Pm9's flush fit magazine is anything but flush and has been known to pinch my thigh in my car when I brace my leg against the center console when driving curvy mountain roads...
But sig isn't perfect. The magazine's baseplate is larger - not just width, but length:
Because the sig's magazine sits farther back, it tends to hang up on my palm when dropping unless I change my grip. The Pm9 magazine glides out unobstructed with my natural grip.
The sig's extended magazine is also hoof-shaped on the bottom. The extension really isn't long enough to give my pinky a good grip, so it winds up wrapping underneath it like with the flush fit. Unfortunately, that hoof/horseshoe shape really chafes my pinky during recoil:
Trigger: I love the kahr's long smooth trigger. There is no wall, it basically comes as a surprise each time the trigger breaks. But the reset is very long, and that really slows me down (and gives me more opportunity to drift off target when my technique wans)
The Sig's trigger feels cheap to me. About half of the travel is empty freeplay. Then it has a very short, reasonably smooth, bit of travel until it breaks. Reset is very short, but almost excessively tactile. It just feels cheap to me. I have the 2nd generation of striker design, which has a very dull springy sound when dry firing. Again, it sounds cheap (but it beats a broken striker).
For a pocket gun, I really don't like how short the unfree travel is on the sig's trigger. But I do seem to shoot it better at the range... I'll have to be extra vigilant and won't trust softer holsters like the fabric Uncle Mikes...
Sights: The 3-dot truglo sights on the sig are pretty nice. I definitely like them more than my PM9's standard "dot the i" - faster on target plus glow in the dark. Of course the pm9 has optional night sights too, mine just wasn't so equipped...
Weight: The PM9 is a tad bit lighter, even with equal number of rounds loaded. I was concerned the extra weight might make my jogging shorts ride low, but I honestly don't notice the difference.
Reliability: The PM9, after being modified with lakeline followers (and doing a little dremel work on them), runs 100% with everything I've thrown at it. The P365 has had two failures go extract out of a box of 50 Winchester steel fmj. It has fed everything else just fine - 500 rounds and climbing.
I do notice the P365's followers are showing some wear where the casings rub. I'll keep an eye on it, but this may eventually need Lakeline followers too (paging @Alfonse )
Takedown: Sig wins hands down. Lock the slide back, rotate the takedown lever from 3 o'clock to 6 o'clock, and the slide will slide right off. No need to pull the trigger! No wiggle/struggle to get the slide off like occassionally happens with the PM9. No tool needed (although my Pm9 is broken in enough I can push the takedown pin by hand).
Detail strip: Too close to call. The striker assemblies takedown pretty much the same, though the Sig's backplate is under much less pressure and not likely to shoot springs across the workbench. But the sig needs a punch and hammer to disassemble the extractor. For the trigger group, the sig wins in that it is part of a unit that can be removed relatively easily with the glock tool. For detail cleaning, this is as far as you really need to go with the sig. With the kahr you are probably better off spraying MAF-cleaner, but if you have the dexterity of a watchmaker you can push a couple punches out, unscrew a couple torx screws, and then carefully take out components mostly piecemeal.
Reassembly: Close, but imo Sig wins, mainly due to the fully captured recoil spring assembly. The PM9 needs a minor struggle to get the open-end of the spring lined up just right and to keep it from binding while compressing it enough to put it in place. Reassembling the sig slide is much easier. But with the sig that you need to make sure the takedown lever is still at 6 o'clock. If it has wiggled up during cleaning, you do have to hold the slide lock lever up while rotating the takedown lever back down - a slightly awkward operation.
Overall: I love my pm9 and will keep it as a backup & occasional range toy, but the P365 is definitely superior and has taken over as EDC (or will once my CCW is modified). The most noticeable difference is how much faster I can clear a dueling tree with the p365...