Actually, having run an Invision Board before (though I left it on default setting), I'm fairly certain it's posts and the number of posts required can be altered by those that can access the Admin CP. I also think you can have a different number of posts to make a topic hot in different boards!
EDIT: and actually Danny, phpBB is posts. I just had a look in the Admin CP of my phpBB and it's currently set to 10 posts but I can change it if I want!
EDIT 2: phpBB does have less features, though I've never found it to be seriously lacking anything, but it also has the most important one from my point of view. It's Free!!!
