When comparing Travis vs Bamboo, the Slant community recommends Travis for most people. In the question“What are the best continuous integration tools?” Travis is ranked 6th while Bamboo is ranked 14th. The most important reason people chose Travis is:
Travis is free for all public repositories on Github.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Free for open source projects
Travis is free for all public repositories on Github.
Pro Easy to set up and configure
All that is needed to set up Travis is a configuration file (travis.yml) in the root of the repository where it will be installed and Travis takes care of the rest.
Pro Github integration
Travis registers every push to GitHub and automatically builds the branch by default.
Pro Supports most technological stacks
Supports the most widely used technological stacks (Node, Ruby, PHP, Python etc...) for free.
Pro OSX & Ubuntu support
Travis' VM are built on Ubuntu 12.04 64 bit Server Edition, with the exception of Objective-C builds, which are based on Mac OS X Mavericks.
Pro Multiple test environments for different runtime versions
Travis supports testing for different versions of the same runtime. All it takes is some lines in the travis.yml
file.
Pro Supports more than a dozen languages
Support for C, C++, Clojure, Erlang, Go, Groovy, Haskell, Java, JavaScript, Perl, PHP, Python, Ruby and Scala.
Pro Great community
Travis CI has a large and helpful community which is quite accepting to new users and provides a great number of tutorials.
Pro Private repositories and personal support w/ TravisPro
Starting at $129 you can use TravisPro, that adds the option of closed-source, private, repositories and personal support.
Pro Excellent website user experience
Pro Fine-grained control over each environment the project needs to be deployed to
Bamboo is the only build server to offer first-class support for the "delivery" aspect of continuous delivery. Deployment projects automate the tedium right out of releasing into each environment, while letting you control the flow with per-environment permissions.
Pro End-to-end visibility when linked to JIRA, Stash and HipChat
When connecting Bamboo with Stash and JIRA, details like JIRA issues, commits, reviews and approvals follow each release from development to production. If HipCHat is part of the integration, team members get notified right away in addition to email notifications.
Pro Integration with Docker
Bamboo allows using Docker containers to create build agents. Using Docker agents lets you run multiple remote agents on the same host without conflicting requirements. It makes it easier to duplicate and distribute changes to build agents, and to use scripts for creating and maintaining agents.
How can you define and build your own image and push it to a registry to share? This is when Bamboo’s Docker tasks come into play. Docker tasks make it possible to build an image, run a container, and push a Docker image to a registry from within your build or deployment project.
Pro Out-of-the-box support for Git branching workflows
Bamboo allows you to automatically detect and build new branches, merge branches together when tests pass and continuously deploy code to staging and production servers based on branch name.
Pro Test automation
Out-of-the-box features that let developers perform parallel testing on elastic agents and quarantine flakey tests.
Pro Easy enterprise-grade administration
Avoid plugin hell by having most important capabilities as out-of-the-box features, not plugins. Bamboo is not just built for teams, but teams-of-teams. It has the administrative features you need to manage and maintain CI at scale. Enterprise model for access control, management, and support.
Pro Bundled AWS CodeDeploy task
Deploying applications with AWS CodeDeploy was always possible by using Bamboo script tasks, and it's now an easier process with a bundled add-on and its accompanying CodeDeploy task.
Pro Integration with Amazon S3
Bamboo can also be integrated with Amazon S3 for unlimited storage.
Cons
Con Only partial .NET support
.NET support is limited to .NET Core and Mono.
Con Only GitHub support
It does not support BitBucket. So it's not in list for companies using BitBucket private or public repositories.
Con Relatively expensive
Commercial plans for Travis are relatively expensive compared to other tools. They start at $129/month.
Con Non-free for private repos
Travis CI was first built to serve and help Open Source Projects, but now they also have added support for Closed Source which unfortunately is not free.

Con No Windows support
Travis can only run tests on Linux and OS X operating systems; running tests on Windows is not currently supported.
Con Very limited basic license.
Although they have $10 license it is very limited even for modest shops. Even next step of commercial license is very expensive for what you get.
Con Bamboo Cloud is going away in Jan. 2017
Migration to Bamboo Server is non-trivial and may not be worth the effort.
Con Free open-source require application to use
Bamboo does offer a free option for open source projects though it requires the user to apply for it in order to use it past the free trial.
