What fundamental new is for new UI comparing with 3.6? I use Firefox for some way, only for firebug mostly. I think its just evolution of person, now I use what is most serves my needs.
Tab Groups are cool, but I don't think anyone uses them. If you're on Windows 7 it hides the menu bar for more vertical space. It has support for lightweight extensions (called "JetPacks" internally) which don't require a restart to install or uninstall. There's no statusbar, like Chrome, URLs pop up when you hover over a hyperlink.
The main advantage over Chrome is that it doesn't freeze up when it's loading a new tab.
I use Tab Groups mainly for task related stuff, as well as using a tab group to allow for a read later style of interface. But no, it's not a major thing for me, I've used Chrome for the past few months and not missed Tab groups.
Tab groups would've been much better if they showed all the tabs across all windows (like Expose on Mac does for windows). Unfortunately it's just a gimmick in its current implementation.
Firefox also hides the menubar on linux, although it can also be disabled. It is also posiblse to enable an 'extension bar', which takes the place of the status bar for extension icons.
Arguably, having the menu visible is not the default setup, is it? The default fold-out "Firefox" menu simply doesn't have that issue and is not transparent.
I agree it's a problem in Thunderbird, which has a menu by default.
I think that if you try to tweak Firefox 4+ to look like 3.6 you're going to run into suboptimalities. It evolved. I think that if you get used to the changes, they're actually changes for the better (new menu giving more vertical room, tabs-on-top, etc).