Bamboo

Bamboo is a continuous integration application of Atlassian. It integrates with HipChat, Stash, JIRA, BitBucket, FishEye, Clover.Confluence. It works great alongside JIRA and Stash providing a fully traceable deployment pipeline.

JENKINS

Jenkins is an award-winning application that monitors executions of repeated jobs. Jenkins can integrates with JIRA, Stash and FishEye but they are all maintained separately as a plugin.

BitBucket

BitBucket is code hosting services that help to manage your public and private git repositories. BitBucket provides a solid service for developers wanting to share and collaborate on projects.

BitBucket Pipeline(Beta)

Bitbucket Cloud is now introducing Pipeline (beta) that let your team build, test, and deploy from Bitbucket. Built right within Bitbucket, giving you end-to-end visibility from coding to deployment. With Bitbucket Pipelines there no CI server to setup, user management to configure, or repositories to synchronize.

Comparisons 

Jenkins have two plugins job-dsl-plugin and workflow-plugin. These two plugins enables Jenkins with Groovy DSLs. All of the DSLs can be stored in VCS and changes can be properly audited and reverted if needed. job-dsl-plugin also supports job templates which reduce a lot of manual configurations.

Bamboo however, has CLI to overcome its bulk change restriction. Bamboo CLI interact with bamboo remotely with a series of Cmd execution. It's very hard to determine how to add a new task with it hence lacks of flexibility.

Bitbucket repository is user friendly as you can clone your project, create branches and make pull request and you can also set reviewer on your code.

Bitbucket pipeline (beta) is a enhanced version of bitbucket. It shows statues of your build branches, commits and pull request. It makes continuous integration more effective

Pricing Support 

Jenkins comes in both free and enterprise. The commercial support of Jenkins Enterprise comes from Cloudbees. The price can not be compared here because Cloudbees has not mentioned the price at their site yet.

Bamboo is commercial software. It is free for 30 days. For small team $10 it provides up to 10 jobs at a time, unlimited local agents no remote agents. For growing team it cost $800.

Bitbucket and bitbucket pieline is free for small team, for big team is $10.

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