UBB.Threads is a PHP/MySQL forum, whereas UBB.Classic was a Perl/Flat File forum, UBB.Threads in every way will be faster and less server-intensive than UBB.Classic ever was, because of how things are retrieved and built.
It'd be odd that they're complaining about UBB.Threads and never did with UBB.Classic...
Also, UBB.Classic had 2 main files that queries where routed through (it's good to keep in mind that, again, all files in UBB.Threads are routed through one file):
ultimatebb.cgi - The CGI builder that outputs the content as it's called from the raw files.
ultimatebb.php - The PHP accelerator which read data from the cache.