I've moved our forums to Xenforo a few years ago, by the creators of vBulletin. It's alright if you liked vB but it doesn't seem to get much updates, but that might be because it's "finished" software.
I also tried some years ago to install Discourse but you need all kinds of server setup for that, too complicated to be an alternative to "old fashioned" PHP forum software. And that's before going into the UX, which is more webapp than old fashioned forums. I'm glad I didn't push through with that migration.