I've never used Trac for tickets. My first introduction to Jira was replacing 5 different in-house ticketing systems covering systems, desktop support, to software development. Here are some of the things I've noticed that I haven't seen other ticketing systems do as well; each department's tickets had their own fields that were unique to them, you could pass a ticket department-to-department with a clear interface to map and update fields, a clear history was preserved when going from department to department, you could have a simplified interface for users (with additional, more intimidating fields for people working the tickets), you could update tickets by replying to emails (seems obvious/trivial, but that feature is often missing), search was very good. This was close to 10 years ago.

Fiddling with Trac tickets right now it seems like something I would love if I spent the time to learn. For example, search is just a text field. I imagine if I learned the syntax it'd be very powerful. I remember Jira, at the time, had a "simple search" with separate auto-completing fields for things like opened-by, assigned-to, open-date, and "complex search" that used a text-based syntax.

Not that Jira was amazing, but UI makes a big difference. A coworker showed me a different frontend someone had built in front of BugZilla and it looked 100x more approachable.

After working at places that didn't use Jira (well, almost all of them evaluated it but deemed it too expensive and too large of a project to migrate) my current job uses Jira, again. Man is it slow (I've heard this is growing pains of converting a codebase designed to run on a single server and making "services" out of it to scale) and there's way more confusing integration. I've been trying to use it as little as possible.