This is really an update so that folks arriving at this question aren't misled.
Wordpress.com used to run on LiteSpeed. And WordPress.org used to recommend LiteSpeed.
The reason was simply this:
Like most popular PHP applications, WordPress is written for Apache, which serves more than half of the web. However, WordPress.com sysadmins got sick of Apache crashing at super high workloads and especially when deploying configuration changes. So they chose a superfast and superstable server (LiteSpeed) which is Apache compatible - i.e. is a drop-in replacement, i.e. just simply works using Apache settings including virtual hosts and .htaccess files.
The problem was that LiteSpeed was commercial, and WordPress felt some pressure to live up to its OpenSource ideals (LiteSpeed was commercial....a much more limited "Standard" edition was available for free). So, in 2008 WordPress.com moved to nginx and WordPress.org dropped its LiteSpeed recommendation.
In mid-2013, OpenLiteSpeed was released as an open source edition of the web server. Compared to LiteSpeed Enterprise (the commercial edition), OpenLiteSpeed does not have 100% Apache compatibility (e.g. .htaccess is not supported, Apache rewrite rules are supported but must be copy-pasted from .htaccess into the config), control panels support (can't have cPanel, Plesk, VirtualMin etc on OpenLiteSpeed), mod_security compatibily and page cache (Enterprise edition has page cache for static content while OpenLiteSpeed doesnt...though OpenLiteSpeed can be used with Varnish so this is not a major hurdle).
So, with that background, the advantages of LiteSpeed over Apache:
- It is generally believed that most servers, including Apache, nginx and LiteSpeed are mostly comparable in performance of dynamic content.
- At very high concurrencies, LiteSpeed is faster than nginx which is faster than Apache.
- LiteSpeed and nginx are fantastic (and way ahead of Apache) at serving static content.
- OpenLiteSpeed is really adopting some new, cool stuff like Google's SPDY protocol while Apache lags in implementation.
- LiteSpeed will also likely use a fraction of the resources that Apache uses for the same load...