Looking at the the crops that people have posted, it's my personal belief that Capture One's rendering is not much better than Lightroom, if at all. Frankly, they both look ugly. Capture One's rendering seems to preserve essentially the same amount of detail at the edges, whereas they produce different types of artifacting on uniform areas (such as the man's suit). It could be due to compression artifacts, but there is this nasty criss-crossing line pattern on the C1 4 crop, which seems most apparent in the upper right hand corner of the married couple crop (the corner of the window in the background). In my opinion, C1 4 is producing some fine-grained artifacts that's being mistaken for extra detail. Would either type of artifacting be visible in a print? In theory, the C1 4 rendition may be better, since the artifacts are smaller and may be less visible, but I don't really know.
Honestly, if you're interested in precise noise reduction, don't bother with any of the current RAW converters out there. I think it will be a long time before we see the sophistication and noise profiling technologies of programs such as Noise Ninja or Neatimage (that is, incorporated into the actual program, rather than a third party plugin, such as Noise Ninja for Bibble... which requires a licensed version of Noise Ninja to provide the best functionality).
The best chance of seeing good noise reduction employed by the current leaders of RAW converters will come in the form of a third party plugin... or someone completely new that knows how much photographers value quality noise reduction if they shoot at high ISO. Unless you're analyzing the noise patterns of your own specific camera and generating accurate profiles with a target, the generic noise reduction of ANY raw converter is a fudge at best.