Both are good platforms, it all comes down to preference. Heck, throw the S&W Bodyguard .38 in there as well (my sister owns one, and she is a scary good shot with hers).
J Frame triggers will typically smooth out after a thousand cycles or so. I cleaned and re-oiled the internals of mine one time 7 years ago after I had broken it in and the action is pretty smooth now. Still a little stiff, but not objectionable.
Most people do seem to prefer the LCR trigger. Most I've handled have been quite smooth, though I still don't care for the rather weak, wimpy trigger return. A lot of folks overlook that aspect; I personally prefer the firmer return of the J Frames, particularly since that is what I'm used to on all my other revolvers (Rugers, S&Ws and the lone Taurus and H&R).