I may not be qualified to comment here, as I actually own and have used both!
I use the LCP a lot more, simply because it lets me conceal carry when I have no dress option -- my employer requires a specific style of dress that includes tucked in shirts, ties, dress pants, etc. and if you carry here, you better not ever get caught!!
The LCR, as well as my various J-Frames, simply are too bulky to meet my requirements.
As to those who denigrate the LCP -- it has never failed me, running flawlessly through hundreds of rounds. As for those who laugh at the .380 -- it is certainly not my first choice for CCW, but it is a whole lot better than harsh words and a dirty look!
When I can dress as I like -- I carry .45 ACP.