Disclaimer: The following is personal opinion and worth exactly what you are paying for it.
The K-frame was designed and intended as a platform for the 38 Special cartridge. When S&W wanted to shoot heavy loaded 38 Specials (38/44) they went to the N-frame...the Heavy Duty and Outdoorsman.
The J-frame was designed and intended as a platform for the 32 caliber if I'm not mistaken but was stretched to take 38 Specials by reducing the cylinder to 5 holes from the original 6.
The K-frame is an absolute delight with 38 Specials, from target wadcutters to +P defensive loads. The J-frame is doable in 38 Special although in almost 20 years of firearms instructing/training I never saw or met anyone who could shoot one really well when pushed to go very fast. I personally can't shoot the little guns as my hands are either too big or just shaped wrong. After a very brief stint with them in my early LEO career I gave up on the J-frame and haven't owned one in years.
As for 357 Magnums, yes the K-frames are made to take them and countless people own and shoot them. Tens of thousands of rounds of full Magnums are fired through K-frames (at least on the internet) with no ill affects. And yet, there is a reason why S&W came out with the L-frame. That was a major financial investment on their part and there was a real, not imagined, reason behind it. Magnum ammunition is hard on the K. Simple as that. I personally saw many examples of it at my department with their M-66s.
But when it comes to the J-frame I sincerely believe the 357 chambering is a classic case of, "Just because you can do something doesn't mean you should!" Chambering J-frames for the 357 was purely a marketing ploy, nothing more.
Finally, and I know this is going to start an argument, metallurgy hasn't change all that much. There are no new, magic, lighter and stronger secret alloys out now. Do a little research. Gun steels are pretty simple and the same series of carbon steels and stainless steels are being used as in the past. Better heat treating may have made some difference but science and engineering have had a pretty good grasp of materials and their use for the past 100 or so years.
YMMV,
Dave