FireFox is an entirely new browser, but uses the Gecko layout engine used in Mozilla. Personally, I've found that it's loaded with bugs. In particular, it has problems with CSS padding which has given me lots of headaches lately, and it randomly suffers from a "sticky Alt key", so when you're typing in message boxes, it opens menus like crazy and you have to Ctrl-Alt-Del to kill the background launcher (closing the windows isn't enough if you have quickstart enabled). Blech. I hope they release v0.9 sometime soon.
Netscape should be left to rest in peace. It would be nice to have a properly designed browser using Gecko, but Netscape 6 was little more than Mozilla with lots of crapy toolbars thrown in.
I like Netscape 7.1 but it fails on some things that 7.01 did fine. Like playing embedded sounds and handling the MARQUEE tags correctly.
It never ceases to amaze me how many people still use those tags... or don't even bother to check for parsing errors. Browsers should just ignore blink and marquee tags these days.
One feature I'd like to see in a new browser is a warning that lets you know if the document doesn't parse correctly or has nesting errors. Something unobtrusive, like the little "X" in the lower-left of the Mozilla browser when there's a Javascript error. Nobody really wants to post broken HTML, and I wish my browser would tell me if there's a essential compliance error without having to use a 3rd party tool, like CSE Validator.
Of course, the WYSYWIG tools can use some help, too. That Bill Mumy page was apparently made with a Microsoft tool and then edited by hand, so it doesn't surprise me that it doesn't work in Netscape.