Everyone has a different idea as to what it means to be Agile, I'd be very surprised if the QC Agile accelerator gave you anything useful without a lot of configuration in which case you might be better off just configuring the base product.
JIRA on the other hand has quite a large active user base creating plug-ins. Chances are with JIRA you will have a choice of plug-ins that give JIRA a more Agile feel and one of them may be a fit for your organisation.
But of course both JIRA and QC are highly configurable either one should be able to be made to work with whatever your company calls Agile.
You really need to look at how your company approaches Agile and work out what you need the tool to do before mankiing a decision.
I haven't looked at JIRA, but I have spent a little time looking at Agile Accelerator.
I've read the available documentation, and I downloaded the free Basic version. Agile Accelerator is basically a customized project file. You import the project into your QC system and then use it as a template for creating new projects in which you want to use the Agile model. There is no provision for applying the customization to already existing, populated QC projects.
The AA project customizes the Requirements module to follow the SCRUM model for epics, stories, tasks, sprints, backlogs, etc. They also provide pre-built customized reports that go along with the model, like Burndown charts.
If you pay for the Advanced version, you get access to the more "advanced" elements of the model, like story points and velocity.
It's really just a highly customized QC project, modifying the workflows and modules and reports to make them align better with the Agile SCRUM model.
My company is looking at Agile tools right now, and we already use QC for test management (mostly manual). So we are interested in how the tools we look at will integrate with QC, and also with our defect tracking system and our source control system (which are both separate from QC). I'm not part of the team evaluating the tools, but I'm a technical advisor on the integration with QC.
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