This depends a lot on what you intend to do.
I have run and hosted a large number of forums
- Three forums in MyBB, two at around 100k posts and one at ~2M posts (about to convert to Xenforo)
- Several forums in SMF, the largest at ~15M posts (going to convert to Elkarte)
- Three Xenforo forums, the largest at over 500k posts
- Several phpBB forums, the largest at over 500k posts (converted to MyBB).
1) The weight of raw requests to the forum itself. Often, this is negligible except for poorly designed software. bbPress is the only one that ever struck me as a serious offender here. For software that still uses standard pagination, that means it's still using offset, and until forum devs get away from fixed page starting points this is always going to hurt. There are other ways forum software can screw up, however.
2) The weight of integrating and extending forum functionality. This is relevant when considering things like live/active notification, chats, and so on. I feel like Xenforo is close to the top here but not the fastest.
3) The quality of the database design and how well it scales. Xenforo does pretty good here - it's a modern design whereas most previous software has a lot of cruft built on the expectations of 20 years ago.
Right now my MyBB forum is collapsing under its own weight, and performance is a big part of why I'm moving it to Xenforo. It's a fraction of the size of my SMF forum, with fewer active features, but it just cannot keep up even though it's on the same hardware.
It's hard to give a hard estimate as to Xenforo's performance because the main forum I have to compare it to insists on using a lot of comparatively inefficient addons. Chats that don't bother checking if the window is active, etc. Despite this, it is certainly outperforming MyBB at scale.
In a few months after I get things running I'll be in a much better position to compare SMF/Elkarte to Xenforo performance wise.