There are some universals though. Fast. I hate waiting 10s for page loads in Jira or anything really, if I'm searching for something.
Good data export. Jira is very good with this. You can get XML with all the information, IDs, relationships between things, comments, etc in a single call.
With this I can create a tool personalized for my particular use of the issue tracker, and only go to the issue tracker's website for non-routine tasks.