Do people prefer journal entry approval permission on roles, or doing a journal entry approval workflow?

It kind of depends on the situation. What is prompting the question? A particular situation you are having trouble with?

My Accounting team wants to have some approval process for JEs. I think having roles have the permission to approve is the best route, but they want to know the best process. The other option is creating a workflow that a supervisor of a specific person has to approve and then their supervisor approves, etc.

The downside of the latter option is that you're now waiting on a single person to approve, which could cause backlogs depending on that person's schedule. If you find that your JE's need that level of scrutiny, then it's doable, but that's just a potential problem to watch out for. Otherwise, there's no problem with doing BOTH of the suggestions above - because really you should have already set up the roles so that the appropriate people do & do not have the approval-ability. That's just a great safety net if anything.