I have been using the release candidates of Firefox 3 on Linux for some time now. The experience has been quite good so far. I would encourage you to try it out for yourself - in fact, download it on the 17th of June and help Mozilla set a world record.
Firefox 3 comes with quite a lot of fixes and improvements. The "Field Guide to Firefox 3" is a nice page summarising the more important improvements. It seems to have improved a lot in terms of memory usage and speed. You just have to use Gmail to see the difference in speed for yourself. Since I never open too many tabs, use too many extensions or keep the browser open for too long, I have never personally run into memory-usage issues with previous releases of Firefox and I can't really say if the improvements in this area are that drastic.
One of the more important fixes for Indian users of Firefox on Linux is its improved support for complex text layout, which is used in quite a few Indic scripts. I have complained about it before and I am happy to report that it now seems to work fairly well:
Devanagari Text Rendering on Linux: Firefox 2 (left) v/s Firefox 3 (right)
The composite screen-shot above shows the difference between Firefox 2 and Firefox 3 when rendering Devanagari text (from Josh18) under Linux. I have circled some of the words that were rendered incorrectly by Firefox 2 and correctly by Firefox 3. (Click on the image above to see a larger version.)
It has not been all wonderful though. There are still some issues that make my experience with Firefox 3 less than ideal. The most egregious of these is how some web pages using Flash either cause Firefox 3 to freeze up or just crash with a segmentation fault (of course, this could be due to a badly-written Flash Player plug-in). The other issue that has persisted from Firefox 2 but now seems to have become worse for me is how Firefox would just freeze for a second or so every now and then, especially noticeable while scrolling up and down large web pages. This might be related to garbage-collection cycles, but I am not sure about it.
Incidentally while Firefox 3 itself mercifully does not require GNOME (I am a happy KDE-only user), its new crash-reporting tool does need a few of the GNOME libraries. This tool is now based on Google Breakpad. I found that the crash reporting tool itself would crash while trying to send a crash report to Mozilla. That was fixed only after I installed GConf, ORBit, libIDL, D-Bus and dbus-glib. It still failed to send the crash reports and it turned out that I must also install and configure Curl. Of course, ordinary Linux users with a typically-bloated Linux distribution would not run into such issues.
By the way, there is now a new pseudo-URL named "about:crashes" that would let you to lovingly admire the crash reports that your instance of Firefox has generated and submitted to Mozilla.