Both Jira and Redmine are very powerful tools, so ultimately there's no wrong choice, and it mostly boils down to personal and team preferences.
Having worked with both, I found that I personally prefer working with Jira overall. Here are some of my reasons:
- The out of the box functionality in Jira is decent. The Slack and Github integrations are quite strong.
- Jira has been built with the concept of 'sprints' in mind, which helps if you're running an Agile Scrum team.
- Release management is baked into Jira in a very user-friendly manner, so things like tagging and versioning can all be done in one place.
- It is ubiquitous in the software development world. Most developers are familiar with Jira to some degree, so you can get going faster, if velocity is relevant.
- Confluence (Another Atlassian tool which is often paired with Jira) is quite powerful for internal documentation.
For balance, here's one thing I dislike about Jira:
- Jira has the concept of "Company managed" and "Team managed" projects, which behave quite differently. This can be confusing for team members working with both types of project.
Your mileage may vary!