I use LiteSpeed as my primary webserver. It more or less replaces Apache in most functionality (including rewrites and bytelogging), will drop directly in with CPanel/WHM. It has an extensive featureset really designed for performance and scalability (and DDoS mitigation). The web interface is nice versus digging through configuration files. My favorite feature is the PHP SAPI module they provide which increases PHP performance. I really find LiteSpeed to be a refreshing change from Apache and gives me only the functionality I need to host my personal sites. There is a downside however, Litespeed costs money. The standard version is free (which is what I use), but it caps max concurrent connections. One of my sites is active with hundreds of simultaneous users and I never run into concurrency problems.

I would say LiteSpeed's strength lies in static fileserving and dynamic content with either Python, PHP, or Ruby (especially Ruby on Rails). In older benchmarks it performs better which in my experience is true, but at the same time tuning Apache can get close to similar results, but the LSAPI module is pretty unique (similar to fast-cgi) and works well. The main developer is really attentive and implemented a few things I needed in LiteSpeed.

I'd say give it a try. It can import your existing Apache configuration and run on an offset port and is free unless you need the Enterprise edition.