I haven’t noticed much, if any, difference in accuracy shooting .38’s through my .357’s, the rounds are very accurate for self defense and target applications in a wide variety of guns. I shoot maybe 75 .38’s and 25 .357’s out of every 100 I fire through my .357 magnums, I prefer not to beat myself up all that much anymore.
As the owner of a few 5-shot snub S&W revolvers in steel and alloy, a SP 101 .38 and a new 6-shot Colt Cobra .38, the Cobra is by far the best of the lot when it comes to all-around carry-ability, shoot-ability and conceal-ability.
The King Cobras are more like my 3” K frame S&W Model 13 than it is to the 2” snubs; somewhat larger and heavier, but with the plus of the .357 Mag option. The KC’s will also shoot much nicer at the range with the .38’s than the snubs will... but the Cobra .38 is not a bad shooter at all. The trade off is more weight on the belt and a little bit more bulge under a jacket.
If you can, before you plunk down $600 to $900 (or more!) for a revolver try to handle all that are available and see how they might fit into your intended role. You may be turned off by the weight of a full-lug KC for everyday concealed carry...or you may find it’s perfect! Only a side by side comparison will really let you see how they feel to you. (If you can shoot them that’s even better!)
Guns ain’t cheap, nor are they very easy to come by, during this panic buying frenzy. I’d hate to see you buy something you end up not liking
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Good luck with your search. Stay safe.