I have three 357's (and a .38 snubbie I almost never shoot). Two 686's, and one Python. I shoot the 4" 686 the most. I mostly shoot 38's because loading them is dirt cheap (comparatively) and they're plenty fun to shoot.
The reason why I don't have a .38 to shoot 38 ammo is because they tend to be lighter and have a less balanced feel to me.
In the 4" barrel, I find the recoil of full-power 357's to be a bit much after a few dozen rounds. I'm an old guy these days and get plenty of enjoyment out of shooting 38's. No longer do I need to throw a 4-foot flame every time I pull the trigger in order to extract enjoyment. I shoot what I want to shoot - I am not encumbered by expense. I'm just good with the lighter stuff these days. Don't get me wrong, I usually finish my day at the range with a couple cylinders of the hot stuff ;-)
I load the full spectrum of ammo - from very tame wadcutters to top-of-the-scale magnum loads; and everything in between. All are fun in their own way. That's the beauty of .357's - the range of ammo is unmatched. And the loading process is easy, fun, and less persnickity than semi-auto stuff.
If I could own only one gun (heaven forbid!), it would be a .357. Due to ammo versatility.