I was always a MyBB fan, I still like it, but you have to give the nod to phpBB as it's still actively supported, whereas MyBB...they're a little slow to work on things.
The one major thing that annoys me with MyBB is that by default it isn't mobile responsive whereas phpBB is. Yes, you can get a theme for MyBB that is mobile responsive but out of the box a fresh install isn't.
Yep, I know. They were great to use 10 years ago, but not so much today. I did mess around with it a few days ago, installing a theme and stuff. Looked great.
Both phpBB and MyBB are focusing on security updates these days. MyBB 3.0 has been in talks for at least 5 years now. Almost the same for phpBB 4.0. The last time I checked, the 4.0 default theme on GitHub was very stagnent.