I've shot a fair number of nightscapes w/ the A7R II and guess I don't see the same problem, if there is a problem? I looked at both your images. Yes, they're different but I can't tell which one is the best of the two. It could simply be a matter of processing?
There are many small-or-single-pixel white and other-colored spots on the LR version, and no white spots on the C1 version.
Here is a side-by-side of the same lower-left area of each. There is clearly some noise-reduction being applied in C1 that isn't in LR and/or LR is sharpening and C1 isn't.
It might be wise to share the ARW and the TIF here for others to examine. Upload to www.dropbox.com and post a public share link, here.
If I took this sort of shot with my Canon 7D Mark II, I'd have long-exposure NR on, which would take a second shot of identical duration and ISO but with the shutter closed, and then subtract this from the original raw. This tends to get rid of the fixed, single-pixel noise--the tiny spots. Does C1 have access to the camera's hot-pixel map?
Looking at your full sized comparison image, it is quite obvious Capture One is applying some noise reduction. Not only is it removing hot/cold pixels it is also smearing/removing detail! I would say Lightroom is the most honest image coming out of the camera even though it has some noise...
I do agree with the use of long exposure noise reduction (LENR) in this instance or actually shooting a dark for subtraction.
I'm not really surprised to see hot/cold pixels in images off any camera. As part of my initial testing of the A7R II I shot 30 second dark subs at ISO's 100, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200 & 102400 for noise evaluation in PixInsight. I definitely saw a few hot/cold pixels in all the images but don't consider it all that serious a problem. It looks very similar to the noise in images off the A7S, A7R and A7 II, as well as my Canon DSLR's... The use of dark subs or LENR pretty much eliminates the problem. I use all the cameras for astro/nightscape photography with no major concerns as to image quality. The A7R II is very similar in this regard to the A7R.