Personally (and I'm not sure if JIRA fixes this, but Trello gets around it), the biggest issue I have is that Github treats repositories as the only possible context. Say a bug comes in that covers multiple repositories (e.g.: requires a mobile app fix and a backend fix), then you need to create two completely seperate issues and remember to link them manually. This breaks down very quickly. I would much rather issues to optionally exist at an organisation level, with per-repository sub issues stemming from that organisation-level issue.
It also means that someone submitting bugs, say from customer support, must try and figure out where the issue is in order to log it. It's a huge hassle and most just give up and ping an engineer on Slack which is incredibly inefficient.
Trello gets around this by letting you create a "master" issue and link to the individual repository issues. It means engineering can have a bug inbox and triage from there. Still a huge pain and not ideal.
Github also has the "Projects" feature, but it is useless IMO due to the above issue - I wish projects would work at an organisation level.