What do you like best?
There are some really powerful and pretty UI controls, such as the Datagrid (FlexGrid), FlexChart, and additionally some other inputs.
The filters for the Flexgrid is pretty powerful and customizable. There is a lot of sample project you can download to play around with their examples, and their support is also top tier.
What do you dislike?
The license, or purchase, limits you to a certain version of the product at the time, I believe. So if you purchased a license for this year, you may not be entitled to massive version upgrades that they make in the upcoming years. You would have to purchase the newer licenses.
If you wish to stay with your old license, that makes it hard if you refer to the documentation online, it may not be fully compatible (there may be changes it is referring to that you do not have).
Additionally, this is not Open Sourced, so you have to black box the software. Especially with working with an older version of the license, your options may be limited to reaching out to support at times.
What problems are you solving with the product? What benefits have you realized?
One of the biggest problem working with ComponentOne is having to blackbox the software, as it could potentially take up more of your time, "hacking" your way to get it working. Compared to an open-source technology, where you will be able to dive into the source code to potentially figure out why something isn't working, ComponentOne, especially with older versions of the software, require playing around, mindlessly sometimes.
The biggest benefit with ComponentOne is that it is a high-quality library with minimal bugs, additionally, there are many powerful UI bells and whistles that come with it that make it more or less worth working with proprietary commercial software.