C1 is a bit cleaner, I have noticed with night photography work, however, with the details, I find that C1 can't get anywhere near as much out of the files as LR. C1 to me does a great job on the Nikon, Canon and Phase One file I have, but I just don't see the same ability to pull out the details of the Fuji files, mainly in areas of finer details, like tree branches or leaves.
LR gets more details, but I still don't like the final output from LR as the images seem to be too smooth. Rocks especially seem to look very bland to me, no finer details that are there, somehow LR smooths this over, giving the image more of a plastic look. It's not over done noise reduction either as I tend to turn it off on lower iso files, 200 and 400. It's like the finer textures are scrubbed.
As already mentioned by others, LR takes the lens data from the metadata and auto applies it. C1 doesn't so, if you try to combine images from C1 and LR, (I sometimes do this), they wont' align since the LR image has the lens corrections applies and C1 does not by default and if you apply the C1 corrections, they will not be the same as the ones in LR.
LR is very close for my work, but I would like to see more the finer textures come out.
Paul