I have two 340PDs (the older one with the "orange toothbrush" plastic front sight ramp, the newer with the green fiber-optic front sight).
My original intent in buying these, like most who purchase these featherweight little guns, was to have a truly lightweight CCW gun with a really potent cartridge.
When I first bought them a decade or so ago, I shot 20-50 rounds of nearly all available commercial premium .357 Magnum loads through them, in bullet weights from 110 to 158 grains, to determine which loads had the best accuracy and precision.
I'm not "recoil sensitive" at all, but this testing for accuracy and precision wasn't pleasant.
I wouldn't say shooting those loads was exactly painful, but it was not fun by any means.
I do think the .357 Magnum loads give some meaningful increase in terminal ballistic effect over the .38 Special+P loads, BUT...
my experience after prolonged testing was that the better .38 Special+P loads were simply both more accurate and more precise in these lightweight guns than any of the .357 Magnum loads.
I don't know why, and it wasn't a matter of flinching or other problems related to hold stability, as far as I could tell.
In any event, the single most accurate & precise load in these little guns, in my hands, was the .38 Special+P Speer Gold Dot 135gr JHP (no difference between the standard & "short barrel" varieties, as far as I could tell), so that's what I have ever since carried in mine.
As always, "YMMV".
The older I get, the less enthusiastic I am about carrying heavy guns.
Over the past 30 years I've trained and qualified and CCW'd with full size 1911s, HK P7M8s, Sig-Sauer P220s, various Glocks in a variety of calibers, a number of different S&W and Ruger revolvers and other guns, but now, in my seventh decade (and never yet having needed to draw "for real", and being both situationally-aware and cautious), I'm often content to carry the little 340PDx, especially, but not only, in hottest weather.
Best.