If I'm going to have a revolver in an auto cartridge, I think .380 would be my last choice. 9mm would make a ton more sense, and is much cheaper to shoot. If you're choosing between the two listed, I'll take an LCR in. 38.
Those moon clips are a real drawback though for auto cartridge revolver. I'd go for the tried and true .357.
I'd have to say 38spl. I don't see many (actually, never seen any) wheel guns in .380. I prefer them in .357 magnum, as opposed to .38spl, to maximize my fun time with them....
.357. You can have the power of a magnum and shoot .38 Specials. That is a win/win all around.
I do own a .380 but not in a wheel gun. Actually, my wife owns the Ruger LCP.
.44 Special is what I have. Barring that I'd go with a .357 in a snubbie wheel gun.