I think Capture One Pro is superior to Lightroom in everything but the library system that is offered with Lightroom, though what is provided in Capture One Pro is still very good.
I always found the library system in Lightroom to be painful only because of how slow it is. It's hard to imagine enough features to make up for a UI that routinely takes >1s to render images onto the page.
That's what got me to switch off Lightroom, and Capture One's excellent other features kept me on the latter. Highly recommended.
I never got into the catalogs/sessions way of managing my library but Capture One is my favourite processing tool. So I use digiKam to manage my library and Capture One to process the individual photos.
Interesting. Capture One is a non destructive photo editor: how does that not force to use Capture One for managing your library as well? Is digiKam able to access the post-process images from Capture One?
Capture One looks great but it's way more expensive than Lightroom. Lightroom is $120 a year. Capture One is $500 and $150 for an upgrade between versions or $240 a year.
Note that you can buy edition that are limited to one maker (Fujifilm or Sony) for quite a bit cheaper than the whole package. Combined with semi-regular sales/promo code (check the fujirumors or sonyrumors website), you can get a perpetual version for very interesting price: I reckon having bought the Fujifilm edition for about 125$.