Doc - I've probably already stated this at one time or another - I'm old - so I'll repeat myself!
I personally don't think you can go wrong with either. I had a 357 LCR - shot 357s once in it and then stuck to 38s - I just like the 38 cartridge.
I traded it off on my Smith Model 36 snub J frame.
Both - 5 shots. Both can carry 38s. (The LCR has the edge if that's what a person wants to use - 357). LCR - DAO. Smith 36 - SA/DA. Both cylinder swing out loading and ejection.
My preference for the Smith is probably based on the "way" I carry. I am permitted in both AZ and MI. AZ can be open carry (as can MI) but I prefer concealed. I carry on the belt and the Model 36 just seems to "snug in" a little better. True - it has a hammer spur so most wouldn't want it if it is going to be pocket carried due to possible snag.
Both the LCR and the 36 shoot well at SD ranges - neither are "target guns". In the end - either is an excellent choice for someone who is confident in carrying a wheel-gun.
As an example - I have a friend who is 82. He bought a .380 Smith Bodyguard. He and I took the MI class together and I noticed during the range qualifications, he had quite a bit of difficulty in operating the 380 BG. His hands are somewhat "arthritic" and racking it was difficult for him. He has stuck with it but he probably would do much better with a LCR or similar. Easier on the older hands, easier to load, etc. In essence, a revolver such as the LCR or others provide security, especially to older folks, who feel the need to have something and yet it is about the most simple of firearms to load and shoot. Not knocking semi-autos at all - but some are very difficult to rack, magazines can be difficult to load - especially double stacks and even some single stacks, inserting magazines can be a challenge for some, etc. A revolver . . . open the cylinder, slide the bullets into the little holes, close and you're ready.
Long winded . . but in my book . . . an LCR, a Smith or similar are all good. The trick is to practice and shoot it regular.