One phpBB site (
http://phpbb.ulead.com.tw/EN/index.php) that I frequent daily has nearly 23,000 members and there are hundreds of posts daily, so size is not a problem: OK, their server is in Taiwan and sometimes there are speed difficulties there when there are more than 70 or 80 users on-line at the same time.
My own SMF site (
http://www.cypenv.org/smf/index.php) was originally phpBB, but I much prefer SMF for better flexibility and security. It is interchangeable with phpBB so, if your host server supports one, it supports the other. In fact, you can switch from phpBB to SMF in about 10 minutes: there is a script for that purpose! Of course, mine is highly specialised and has few members (about 65, if I remember correctly). This has cost me nothing extra to have the php and MySQL facilities.