What do you like best?
Being part of the Atlassian product family, Bitbucket has access to and works seamlessly well with their other developer focused tools, such as JIRA, and Bamboo. This means, an organization or team can sign up with the Atlassian stack and have an end to end tool chain, and developer experience, without having to look else where, and do patch work to make different parts of their workflow work together.
For example, you can use JIRA for issue tracking, check in codes into Bitbucket with references to JIRA issues, so you can easily see what commits are related to which issue, and then build/deploy with Bamboo, with your build/deploy plans referencing Bitbucket commits, JIRA issues and releases. And for bonus point, you can federate all your user identities with their Crowd offering. This complete tool chain and end to end experience is what gives Bitbucket the edge over other competing products.
Of course, Bitbucket itself is a solid product, with support for both Cloud and on-prem deployment options. Again, this is where the rest of the Atlassian stack comes in, as those applications also support Cloud and on-prem (with exception to Bamboo, which is being replaced by Bitbucket pipeline).
Bitbucket also has very friendly licensing terms for "casual developers" that are just looking for affordable code repository services, as you can use Bitbucket for free, and have private repos, something competing offerings do not have.
What do you dislike?
As a code repository, there really isn't a lot of downsides to use Bitbucket, especially if you are already using Atlassian products for your development. However, there are a few things to keep in mind:
* there are some differences between the Cloud and on-prem offerings, especially when it comes to 3rd party add-ons, so do your homework when choosing which route to take.
* GitHub is still the #1 place for hosting public (open source) projects, and many developers tend to be more familiar with it and its tool chain, so if you want to start an open source project, you may need to take that into consideration.
* It's tool chain with JIRA (issues), Confluence (wiki), etc, is more advanced and powerful, but also more involved, unlike its main competitor GitHub, which is more simplistic but also easier to use.
So it really comes down to your use case, e.g. if it is for personal or enterprise, what you already have as part of your tool chain.
Recommendations to others considering the product
* check if there are any 3rd party add-ons you will depend on.
* if you are or will be using other Atlassian tools.
What business problems are you solving with the product? What benefits have you realized?
Mainly using it as a Git code repository for all of our projects, integrated with Atlassian JIRA, Confluence, and Bamboo to have an end to end automated develop/build/release/deploy process.