GoCD is easy to set up. So if you just want to get some pipelines up & running quickly, & they're quite stable, or you can have many pipelines for different needs then GoCD is great. Still, if you only want to have a few pipelines, but with the flexibility to run them with different parameters dynamically, then Jenkins is better.
TeamCity is well suited for an organization using continuous integration, meaning you release code to production often, and an agile project management system. There are free versions available for small teams and enterprise versions available for large teams with many different builds. TeamCity is probably overkill for basic e-commerce or blog website builds that do not require much development after the initial launch
Pipeline-as-Code works really well. All our pipelines are defined in yml files, which are checked into SCM.
The ability to link multiple pipelines together is really cool. Later pipelines can declare a dependency to pick up the build artifacts of earlier ones.
Agents definition is really great. We can define multiple different kinds of environments to best suit our diverse build systems.
Fully customizable build process. Each step of the build process can be parameterized and customized to address specific needs of particular applications. This allowed us to easily convert from a custom VM-based environment to our current Docker-based environment.
Manages large numbers of build agents seamlessly. This allows us to run multiple builds on many different applications in a most efficient manner.
Build steps can be managed in an arbitrary manner, allowing some parts of the process to proceed in parallel while restricting others to depend on completion of all relevant steps.
TeamCity runs really well, even when sharing a small instance with other applications. The user interface adequately conveys important information without being overly bloated, and it is snappy. There isn't any significant overhead to build agents or unit test runners that we have measured.
I prefer using GoCD compared to Jenkins. The UI makes sense, I like the simplicity to hit the 'Play' button for a straightforward deployment of the 'Play +' if you need to override some settings when deploying whereas Jenkins, you have the whole page for each pipeline. The environment makes sense but can often confuse the user while GoCD simply has a drop-down to select your environment.
Jenkins relies on being open source as the primary driver for its success. This low cost is a huge factor for many companies, both small and large. The professional, free tier of TeamCity offers a huge amount of growth before ever needing to pay anything. I personally also find the user experience of TeamCity to be much better, both from a look and feel, as well as from an out-of-the-box feature set perspective. The big selling feature of ADO is its native integration with Azure. TeamCity integrates very well with out-of-the-box .NET support and greatly simplifies our use of another diverse tooling outside of the Microsoft ecosystem.
Settings.xml need to be backed up periodically. It contains all the settings for your pipelines! We accidentally deleted before and we have to restore and re-create several missing pipelines
More straight forward use of API and allows filtering e.g., pull all pipelines triggered after this date
TeamCity was a key contributor to our organization's adoption of Agile.
TeamCity made it possible to KILL "It works on my laptop" conversations with Developers. If it does not compile in TeamCity - the project is not deployable. TeamCity's easy to use interface made it possible to quickly adopt a "Deploy Only from TeamCity" policy, further ensuring TeamCity Builds were the gold-standard for well-configured source code.