liquid design : what i use that is when a client website have tons of contents / articles in a page and have to spread out nicely. Also liquid design is resolution friendly without worrying who cant view your site.

Fixed in the other hand is easy to code and easy to get your layout done. Usually its used if you are doing a microsite / minimal site..

From my experience, fixed is cross browser friendly and liquid sometimes have min-height problem in IE6.. even though theres workaround for it but not all content i put in works..

Since IE7+ is out, i would say its all friendly now.

usually is em(s).