When comparing Semaphore CI vs CloudBees, the Slant community recommends Semaphore CI for most people. In the question“What are the best hosted continuous integration services?” Semaphore CI is ranked 7th while CloudBees is ranked 8th. The most important reason people chose Semaphore CI is:
Whenever a new push is made on GitHub or Bitbucket, Semaphore automatically runs tests on that branch.
Specs
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Pros
Pro Automatic Testing
Whenever a new push is made on GitHub or Bitbucket, Semaphore automatically runs tests on that branch.
Pro Free for open source
Semaphore supports open source and offers unlimited open source projects.
Pro Complete customer support
Semaphore offers all-around customer support for its commercial users.
Pro Free 100 builds per month for private projects
Semaphore offers 100 builds every month for private projects. This package is free for an unlimited time and offers: free & unlimited deploys, unlimited collaborators and running tests in parallel.
Pro GitHub integration
Projects can be imported from GitHub and Semaphore will automatically connect with that repository, once that's done, it will automatically trigger for every code commit.
Pro Docker support
Out of the box Docker support. Additionally, Semaphore can cache Docker images by using included docker-cache commands.
Pro Easy to configure
Semaphore is quite easy to configure and work with. It easily integrates with GitHub and a first build is only a few clicks away.
Semaphore is configured using .yaml configuration files which can be added from the web UI. There are a lot of tutorials out there that help developers configure Semaphore to their preference.
Pro Great enterprise level support
Quick access to experts who are responsive, helpful, and friendly.
Pro Private and internal SVN and Git repositories
Support for both SVN and Git private repositories.
Pro Highly customisable
Jenkins is by far the most customizable solution on the market. And CloudBees is built on Jenkins. There are over 400 plugins to support building and testing virtually any project.
Pro Free for open source projects
CloudBees offers a solution for owners and developers of free and open source projects to be hosted and built by their service.
Cons

Con Proprietary with private project for $30/month
Semaphore is not free and nor is it open source. Pricing starts at $29 per month. However, there is a free option for private projects which have less than 100 builds per month and it's free for open source projects.
Con Java-only solution (without plugins)
Jenkins supports only software built with Java (unless you use plugins)
