JIRA is a great solution for tracking issues against multiple different projects. It has good integrations, custom workflows, and can function well for internal and external use.
For an external issue tracker on a closed source project, this is a really great tool to allow 3rd party developers to submit, track, and vote on any bugs or feature requests they are interested in.
It's not free, and if you are dealing with a project that already lives on GitHub, you may as well just use the built in bug tracking system there.
Where JIRA shines is where you have some custom workflows and such you want to use, which can be a pain to maintain.
GitHub has a great built in issue tracker, and integrations like Waffle for project management. If you're already using GitHub, and don't need to have a different level of visibility for the code and the issues, use GitHub. If any of that isn't true, give JIRA a serious look.
The best use case for JIRA is to expose an issue tracking system to 3rd party developers. This lets the community submit bugs and features, but it also has a really nice voting system that lets the community help you rank and prioritize things that are important to them. JIRA also has a nice system for setting who can see what, so partners with access to special betas or private APIs can use the same system without exposing data to everyone.