I have a .38special and a .357mag. So, they each get their own diet.
IF I only had the .357mag, I'd probably still stick to the .357mag diet. I have other handguns for cheaper shooting. Heck, 9mm is SIGNIFICANTLY cheaper than .38special, so I'd go that route if cheap shooting was my only concern.
If I could ONLY have a revolver in a centerfire caliber, I'd go .357mag. I'd then use .38special for daily shooting to keep the cost down and use .357mag for fun/hunting when I could afford it.
however, 9mm is still $2-6 cheaper per box than most .38special, and I have one. Thus, 9mm wins the 'cheap shooting centerfire ammo' category.
btw: only .357 in .357 as I then don't have to keep re-sighting in the handgun for the different POI with the different load strengths. AND no carbon ring in the cylinder to fret about.