I use Konqueror in the latest CVS of KDE2 and Mozilla 0.6 when Konqueror doesn't render the pages correctly or refuses to load the page.
The difference between Mozilla 0.6 and Netscape 6 is "bloat"; Netscape 6 is to be avoided at all cost because of blatant banner ads, etc., and it installs a huge amount of cruft that simply does not need to be there. Galeon is excellent, but I'd rather just stick with Mozilla, thank you. The latest Opera beta for Linux isn't too bad, either, but there's no word yet on whether, like its 5.0 siblings, it will be _free_, so I'm not using it as my browser.
Why Konqueror? 1) It's free; 2) it works, by golly, on a majority of pages I visit; 3) it's quite fast, even faster than Mozilla 0.6 on my machines (Celeron 550 and a Sparc2).
Why Mozilla? 1) It's free; 2) it loads practically everything out there; 3) it's decently fast.
AFAIK there is no IE for non-Windows/Macintosh OSes.
My rule of thumb is that if a browser won't build under Linux-2.4.0-test12, Solaris 8, and NetBSD 1.5, then I'm not even going to consider it. =P