Sadly, Smith and Wesson has a history of frame cracking with their Airweight revolvers. Not a huge number, but more than enough to create a level of worry.
If I were you, I carry one of the following: S&W model 640 or S&W model 36. Neither is a lightweight revolver, but neither is so heavy to slow you down on your run.
Many guns have failures... again, not common, but it occurs on all guns. My 642-1, converted to 9mm, has been doing fine for over two years. Plenty of other shooters have done 9mm Airweight conversions... I've yet to see one cracked frame from that.
The problem with running is the mass of the firearm. When it starts moving back and forth, you have to stop it... either by stopping your run or grabbing the item (cell phone, insulin pump, or firearm). Ideally, you want a light firearm for a gun you are taking on a run... for comfort, not slowing you down.
If you have any desire to shoot .357 I'd go for the LCRx, it's a little heavier than the S&W Airlite's and seems better at taming recoil.
But for .38 only, go handle both and see what you like. I love my j-frames, but the LCR's I've looked at are pretty nice too.
Anything LCR related in .357/9mm is noticeably heavier than a Airweight (different frame than the .38). My father has a .357 LCR that I compared to my 642-1 when I was looking at switching. I was considering the 9mm LCR over my 642-1, but decided to convert... saving weight and years of training on the gun.
If they did a LCRx in 9mm, I would have made the switch to get the external hammer.
My understanding out of a short barrel the difference between .357 and .38 is not as great as one is often led to expect.
Depends on the loads... I'm sure you can find exotic loads in either caliber to make the argument stronger/weaker.
How is energy figured out? Energy = Mass x Velocity ^2. So, increasing velocity has a more direct ability to increase energy. That is not arguable.
However, energy that isn't expelled into the target is included in that formula. So, even though you can sit down and figure out what a specific caliber is doing with a chronograph and a calculator, there is that other factor. A high velocity, low mass round may have a lot of energy, but if it goes through a target like an ice pick, no real use.
When I carried my 642-1 with .38s, I shot Hornady CD in 110 grain +P. Good enough round for defense. But when I converted to 9mm, I settled on Hornady XTP 147 grain (standard pressure). Muzzle velocity of the 9mm was identical to the .38 +P... pushing a heavier slug. Same exact gun, so numbers were as accurate as you could get.
Now, out of a 2" barrel... .357 isn't doing that much more than .38 +P. It definitely isn't doing 400 FPS more... in any common load. If someone wants to say that, post up some pictures of the muzzle velocity of a 2" .357 doing 1,200+. Realistically, probably in the 900s. But out of a short barrel, 9mm can edge out slightly in terms of velocity. Go out to 3" or 4" barrels, no contest with .357... but need to build up that speed.
So, yes, short barrel in those caliber is not that dramatic. If you compare .357 to standard pressure .38, yea it widens... but how many people carry it? With +P guns, that is what most people load for defense.