I have two of these little lightweight J-frames.
You'll need to make your own determinations, but in my own considered experience, after shooting between 20 and 50 rounds of ALL premium commercial .357 Magnum JHP loads in bullet weights from 110gr to 158gr vs. several different .38 Special+P JHP loads, NONE of the .357 loads were as accurate or precise as the better .38 Special+P loads.
The best accuracy plus precision of all the tested loads in these 340PDs, IME, was .38 Special Gold Dot 135gr+P JHP.
I'm not "recoil sensitive", and wasn't unduly bothered by the admittedly-uncomfortable sharp impulse of the .357 loads, so I'm personally quite convinced about the innate accuracy and precision of the various loads I tested in these guns.
Take it FWIW, and decide for yourself by trying some load comparisons.
The S&W 340PD and the Ruger LCR currently represent the most extreme balance between "lightest weight" plus "most powerful" CCW revolver options available.
While shot-to-shot recovery is slow, to be sure, it's nonetheless true that for a gun that's "carried much, shot little", the 340PD is certainly a viable choice for some of us, at least some of the time, especially in hottest weather when only a small lightweight gun will do for CCW.