My LGS finally got a rental P365 so I was able to do a side by side comparison to my Shield Mod 1. Here's my $0.02.
Will I be switching EDC guns - no, not yet. I'm waiting for the price of the P365 to drop and then I"ll explore my options
Trigger: No contest the P365's trigger is MUCH better than the Shields (But only slightly better than the Shield Mod 2) .
Sights: P365 wins this one - night sights vs. contrast and a better sight picture.
Grip: This one goes to the Shield - it's slightly narrower and deeper than the P365. It just feels better in my hand. The pinky extension on the 8 round mag gives me a bit more to hold on, but this may change if the P365 had the 12 round mag in it!
Felt Recoil: The range gave me the new Sig P365 ammo to use. It's 115 gr vs. the 124 gr I had in my Shield. Initially the felt recoil was the same (115 to 124). However, when I switched loads the Shield had less recoil than the P365 both with 115 gr. and definitely less recoil with 124 gr. in both. Haven't the foggiest why this would be, unless the 115's ballistics are significantly different.
Capacity: We all know the answer to that.
Will I be switching EDC guns - no, not yet. I'm waiting for the price of the P365 to drop and then I"ll explore my options