Has anyone successfully migrated off of Jira and how did you do it?

I would like to make a case for getting our company off of JIRA. We fight this product all the time to get it to tell us the things we want. I won't get too into all the whys of that, because there are a myriad of reasons to hate this tool.

As far as migrating to another story tracker goes, I'm interested in how other teams of medium size (50 - 100 employees) have accomplished this. I'm worried that bringing this up without some kind of plan will be a large waste of time and that we ultimately won't do anything.