I was fed up with having to switch to a newfangled editor every so many years, having to identify new plugins, having to learn new keybindings. I've used Vim for 7 years (I think) and it came pretty close, but in the end the archaic VimScript language and the lack of async commands was something that was nagging me. I wanted to call an editor home, and hone my skills until I pass away, increasing my arcane knowledge over 10-20 years, learning ever more about the scripting language, commands, and writing more and more specific plugins that help with my tasks.
I still want to be coding in 10 years, but I don't want to switch text editors ever again. Emacs shall be my final editor [1], and that's why I decided to switch. Because I can see Emacs still going strong in another 20 years. I wouldn't want to say that about Sublime, or really any other editor right now.
[1] There's a case to be made that NeoVim is going to be great, and it may well be, but right now I'm really, really, really happy with Emacs + Evil. Nothing is perfect, of course, but the things that bug me are really, really small things that I could probably even fix, if I'd invest enough time; but they don't bug me enough for that.
I guess the real problem is me saving too often. Others may be trying to run a long make from vim and wanting to continue editing or looking through files.
But for CSS/SCSS and JS I find easier to use espresso[1]. That's because it's made for web-dev and I don't need to setup my own workflow. I believe same thing is with Sublime Text. It's better to use for web-dev IMHO compared to VIM/EMACS.
ps. That said, I always believed that the editor is a tool. It's better to learn your current editor's ins and outs than switching back and forth from editor to editor.
Learning Emacs or Vim is an investment, one that last your entire life. I will gladly be less productive for a few weeks to gain much more in the long run.
I can't say that you should switch, or that it's superior to anything, but I think you could at least give it a try. And by this I mean: use it as your only text editor for as long as you can invest (a week, maybe a month). Start with the built-in tutorial, install: ido, web-mode, js2-mode, maybe add yas-mode. Install a nice color theme. Learn the key bindings in web-mode to efficiently navigate HTML documents. Try to perform some tasks using macros. While editing try to forget you even have a mouse. Discover the little things, like "undo" being able to be narrowed to the selected lines instead of global linear history, or the kill-ring (you can paste form previous "cut" operations, not just the recent one).
There's some un-learning and re-learning of everyday tings like the shortcuts for copy/paste or the concept of selection vs. region, but for me it was a good investment. I can't say it'll be good for you, but I encourage you to try - if you won't switch you'll at least get a better understanding of what you like about your current editors.