I still haven't had much time to play with the new Backbox other than using it as my day-to-day OS, same as I had been using Backbox 3.13. So far, I can tell there are minor improvements, based on the fact, that Backbox 4 is based on Ubuntu 14.04, not on 12.04 like the Backbox 3.13 is, that came with the Ubuntu itself.
Few, I would say little glitches, also came with Backbox 4 and again, that's why it is based on Ubuntu 14.04 (system time changes on Windows while having dual boot Backbox 4 / Windows 7, Chromium crashes / freezes when returning back from screensaver), but compared to what Backbox can offer in general, these are insignificant and I would say, as I've tried few distros (Fedora, CentOS, Ubuntu and alike (Backbox, Studio, Xubuntu ...), Kali Linux, Arch), almost every distro has it's own.
Since I do not consider myself as a Linux pro, can't actually tell you if I feel any difference with the new kernel other than the fact, it runs smoothly since the day I've installed Backbox 4 without troubles. Well, I had to repair the Grub, because it didn't recognize my Windows 7 partition after the install (and while I'm talking about installation itself - after the backbox was installed, and my laptop was supposed to reboot, it actually did nothing and hung on empty black screen - so I just turned it off and on, and it was all okay), but since grub-repair exists (something like that), it only took me few minutes to make it work.
But in general, I really like the Backbox 4 so far, it works as it is supposed to, it is stable and reliable, and that's what I want from my OS.
But since this thread exists, quick question - is it possible, to make the backbox menu the way it looked in backbox 3.13? It's not a big issue but you know, old habits die hard