What do you like best?
Resolve is incredible software, at an incredible value: free. Of course, we shoot on BMCCs, so we have received Resolve dongles to unlock additional features of the software, namely: noise reduction.
Resolve has a mostly intuitive interface, and specifics of how to use it, can be found through plentiful online resources. Color grading is made easy through our use of the product. Black Magic provides a helpful and free pdf with their product for users to become familiar with and use to learn the software. I find this awesome, and I'm quite happy with their intentionality with DaVinci, even if their approach with cameras is extremely lacking.
What do you dislike?
One will need some previous experience with the art of color correcting/grading to be even slightly competent with Resolve. Of course, you will grow in your skill over time, but many of the features built-in to Resolve should be somewhat second nature if you are familiar with other grading software built-in to Adobe programs.
Another note is the NLE included in Resolve. I've used it only a tiny bit to become more familiar with it. It's not extensive, and only simply gets the job done as opposed to software that actually costs money.
While this could be useful for someone wanting to try their hand at editing, I don't think it slightly practical for professional use.
Another thing that just doesn't work well is sharing color grading profiles with other users. There is a built-in user sign-in, however it does not transfer over well to multiple users. This should be addressed by cloud-based sign-in, but time will tell.
Recommendations to others considering the product
If nothing else, just try out this software. It really has a ton built-in, and has a huge leg up over the basic Lumetri color grading features in Premiere Pro.
What business problems are you solving with the product? What benefits have you realized?
Resolve has made it easy to provide beautifully colored images for our clients in early draft stages. It's become easy to have one editor cutting together a story for a client, meanwhile, the other colors the footage. With a plethora of exporting options, it is simple for one to replace the footage in their NLE software with the graded footage.