Apache/mod_perl is definitely faster, and would serve much more clients in less time.

Mod_Perl's performance is not just a result of the persistent Perl Interpreter, it also benefits a lot from the Apache server doing all the network and parsing stuff.
In fact all modules using Perl sockets are much slower than anything written in C.

Listen to tachyon about the memory footprint.

But if you don't need that performance boost and like HTTP::Daemon, just use it. ;)