Icecat is GNU's fork of Firefox, while Iceweasel is Debian's fork of the
same. (The folks in the Debian user forums will tell you Iceweasel IS
firefox, except for the name.)
Iceweasel will allow you to install non-free addons, whereas GNU's Icecat,
has a separate page of addons, all of which are free software.
If you like to select search engines for the browser search bar, I doubt you
will find a better selection in any browser other than Icecat.
GNU Icecat also includes several privacy enhancements. There is no need to go
to about:config and delete all references to Google to preserve your privacy,
because Icecat does it by default. You do not have to install the 'HTTPS
Everywhere' extension, because Icecat has it by default. For me, it was the
strangest sense of dejavu when I saw it the first time, because it was as if
the packager had read my mind and altered Icecat by default, in the way I've
have always done by hand, which appealed to my sense of laziness.
With Icecat, freedom is priority number 1 and privacy is a very close second,
in my opinion. Others may see it differently.
