Speed
mod_fcgid seems to be as fast as the traditional mod_php Apache module. However, it also allows to be run on a multi threaded Apache server. For various reasons this still does not work reliable with mod_php4 / mod_php5.
Configuration flexibility
With mod_fcgid it is possible to run many different PHP versions on the same server, and even with multiple different users.
Installation is more complex
Installation of PHP using mod_fcgid is probably more difficult than setting up mod_php5, mainly because there is only a few documentation about it that can be found. However, since you found this document, you may be lucky...
This manual is designed for Debian Etch servers. It expects a server running Apache 2.x. Basically this should work equally for other systems – they probably just use different paths and package names...
The following packages are required:
php5-cgi
This is the CGI binary of PHP5. It was compiled with FCGI support and works perfectly together with mod_fcgid.
libapache2-mod-fcgid
This is the FCGID module
apache2-mpm-worker
This is the multi threaded multi-processing module (MPM) for Apache2. It replaces apache2-mpm-prefork with is a single-threaded MPM and is required by mod_php4 / mod_php5. Of course these packages must also be removed.
Keep in mind that you may want to make a backup of your current php.ini, because php5-cgi will set up a new configuration file.
# apt-get -u install php5-cgi libapache2-mod-fcgid apache2-mpm-worker