Integrating JIRA with HP Quality Center gave our dev team and management a new window to participate/track the defects Testing Team reports from. This integration is absolutely powerful and made defect sharing with different parties a peace of cake. Now we, the testing team, can report defects on our own "beloved" HP QC, and these defects gets sent automatically or upon request to different JIRA Projects and to different project parties and teams.
I would say test management, as it's a generic issue tracking tool, and not designed specifically for test management. So, the only support for test cases is the ability to mark them as passed or failed as part of the test execution, and that's the whole test, not step by step like Quality Center. It does have many test management add-ons that can be bought, and some of them can perform close functionality to what HP Sprinter does, like Bonfire, but it does not provide video recording. It doesn't provide version control for Test Cases, and integration with Test Automation and Performance Testing tools is cumbersome.
I hate the fact that I have to buy an add-on for each feature I need. Some people might see this as positive thing since you buy only what you need, but again, not all add-ons are provided by Atlassian, and hence support and quality is subject to different providers, which is again is cumbersome, and not many people would go on with.
Reporting also needs improvement, as I need to be able to create my own custom reports and be able to export them, and screen shots doesn't work all the time.
If you are an agile development team, go for it. I would advise that f your dev team have problems accessing HP Quality Center, go for it and integrate Jira with Quality Center.