What do you like best?
Capture One Pro is an All-in-One tool when it comes to image acquisition, color-rendition, post-processing, and export. PhaseOne has done a phenomenal job in creating a tool that lets you virtually forgo a post-processing tool such as Adobe Photoshop. Capture One Pro is a tailor-made product for high-end photography outfits such as PhaseOne and Mamiya - and many others. PhaseOne has included everything that's needed for those cameras and lenses, including ICC and Lens Profiles for each back and most all available lenses for those two products. Capture One Pro also has a plethora of supported DSLR camera ICC Profiles and an equally extensible library of Lens Profiles to virtually use this tool for any type of camera / lens combination. Every now-and-then there are complaints about camera's not being supported or lenses not being in the supported list but what people forget is that a lot of these complaints are from people that actually do not use Capture One Pro for tethered shooting (in which case the body/back/lens marriage has to be supported). When a user shoots via an unsupported body / lens to a memory card, those "shortcomings" can be circumvented by simply shooting a high-quality White-Balance target and creating a custom lens profile via a generic pre-existing profile.
Capture One Pro renders colors amazingly well and - even though some would like to disagree - will blow amateur tools such as Lightroom right out of the water. C1 Pro does have a steep learning curve which most Lightroom users do not like - they are used to a one-screen setup with very few (and basic) adjustment panes and become easily overwhelmed with the amount of adjustment-possibilities through C1 Pro. Capture One Pro is a tool geared towards the professional with high-end results and productivity in mind - however, do not expect to master it in one day (sorry Lightroom).
Capture One Pro has two ways of purchasing their license, either via a subscription or out-right purchase or a full release - meaning Capture One Pro 6, 7, 8, 9 etc. Maintenance releases are always excluded from pay and are free - i.e. 9.0.1 .. 9.1 .. 9.3 etc. The release schedule has somewhat increased in pace and what used to be a fairly big span between full release has somewhat shrunk to a once a year (may be slightly longer) but its quality and production value outweighs the cost (which in the scheme of things isn't that much).
What do you dislike?
PhaseOne does an exceptional job hunting down bugs and fixing them, however - since their programmers aren't in the hundreds it has happened that a bug has leaped through one or two maintenance releases. It's not too big of an issue for a daily user who can find his way around.
Recommendations to others considering the product
Don't expect miracles (they may be somewhat possible); just because you Use the best tools out there doesn't mean the outcome will be the best at first. It's the same conundrum with people that buy Leicas and expect award-winning Fine-Art shots without an eye for composition.
Capture One Pro is a beast - plain and simple - and you WILL need time to figure it out. There will also be plenty of times where you're fed up and frustrated because something was "just so much simpler to do" in Lightroom (which is the most common complain you read about in C1 user groups) - and honestly, if that's your go-to answer then you should probably stick with Adobe.
PhaseOne has an amazing tech-support team that will bend over backwards to *personally* help you out - however, some people mistake the user forum as the tech-support and will get upset if no-one answers their plea for help.
Bottomline, if you want great images you choose the best - Gear and RAW Processor.
What business problems are you solving with the product? What benefits have you realized?
I use Capture One Pro as a daily workhorse as a commercial photographer and for private use. Its been THE tool we use from capture to getting files ready for press. We spend a sizable amount of money each year on professional printed catalogs, brochures, and post-cards, and C1 Pro can handle pre-press without any issues.