Who is Capture One for, and what does it do for you?
Phase One would argue that Capture One produces the very best renderings of your Raw files. Adobe, Apple of DxO might disagree and say that their's are the best. Ultimately, the quality that your images appear at has more to do with the time you have to work on them than the brand of software you are using. Capture One excels at workflow. You can move adjustment elements to whichever pane you like, and easily switch from tool to tool with keyboard shortcuts. With version 6 I found that Capture One responded noticeably quicker on the computer I had than Lightroom did, especially when you have a big catalogue of images. Version 7 is slower and more demanding on an old machine. If you have a new machine then pretty much any software is going to zip along.
Where Capture One has leapt ahead, though, is in team photography. If you have someone on lighting, someone on art direction and someone commissioning the shot, then there are a lot of people who need access to the images as they come out in order to do their jobs properly. With wifi and Capture Pilot, anyone on your team with an iPhone or iPad can see what's going on, and if you've paid for the upgraded version of the software you can actually control the shooting from your iPhone.
Digital photography has already taken most of the guess work out of the photo shoot, but Capture One/Capture Pilot takes it to its final conclusion. The make-up artist can now know exactly how their work is appearing on camera, the photo assistant can see immediately whether the shot is in focus or not, the art director can see whether it's going to fit the layout.
This isn't to say that Capture One is only for commercial photographers. It's enjoyable to use, intuitive and powerful, and if you aren't currently bought-in to any particular system, it gives a very creamy, refined experience. In terms of its target market, though, Capture One is fighting hard to be not merely the best choice but the only choice for high-end commercial work.
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