Zimbra Advanced (AJAX) web client uses a *LOT* of JavaScript. Thus, the speed of the browser's JavaScript engine matters a *LOT*.
Google Chrome or Firefox 4.0 beta 10+ will give you the smoothest Zimbra experience. Opera isn't too far behind. Can't comment on Safari.
Firefox 3.x and any version of IE will lead to frustration on any system with a CPU slower than 2 GHz and tonnes of RAM.

The
JS engines in those browsers are glacial.
If you have to use Firefox 3.x or IE, then consider using the Standard web client. You lose some features (like Zimlets), but you get a much more usable interface.