I've been using Konqueror a lot this past year, it is fast and give a much better page rendering than the old Netscape Communicator. Konqueror is over all a great browser though it will choke every once in a while on cascading style sheets. This is as of 2.0, my limited experience with 2.1 seemed to have improved in this regard. It also crashes every once in a while.
In comparison Mozilla 0.9.5 seems much more stable. On the down side Mozilla feels like a Mac truck when it starts up. It takes 22 seconds vs Konky's 8 seconds, and this is while I am not in KDE, which would pre-load some libraries. Once loaded it rivals Konky in page loading speed, they really seem to be neck and neck on larger pages.
Cookie management and proxy configuration are also advanced. And the new tab feature is also very nice -- yes, I know it is a rip from Opera.
I took a shot [cgi-fun.hypermart.net] of the three browsers to give a visual of the three's page rendering. Warning, it is large.