A very popular choice for running Perl web applications these days seems to be behind a nginx webserver proxying requests to either a FastCGI daemon or a PSGI enabled webserver
HTTP is well understood by most system administrators and it's easy to debug. There's almost always some kind of reverse proxy already deployed, so it is a piece of cake to just add another configuration stanza to its configuration in order to bring your application up and running in a few seconds. Never tested the speed differances with both settings but on the other hand i never had any problems in that area, so it can't be that bad.