The classic. Mature, very customizable, runs on almost any PHP host, with a huge extension library.
Modern, real-time discussions and great on mobile. Needs a VPS with Docker, so it is harder to host cheaply.
Lightweight and clean, with an extension system. Good for small, modern communities on shared hosting.
Simple, free and familiar, with lots of themes and plugins. Easy on beginners.
Our take: pick phpBB or MyBB for cheap shared hosting, Discourse if you have a VPS, and Flarum for a modern look on a budget.