The thing about Emacs is really its extensibility. There is simply no other text editor out there that can open a single C/C++ source file and automatically infer all tags (even of included headers) without any kind of project set up. That is simply awesome and to my knowledge only available with semantic-mode in Emacs.
Vim can use ctags or cscope or clang, but that is not the same thing. These are great tools, but they need to be set up with the correct include paths and they need to be run regularly to be useful.
To my mind, that is what makes Emacs so unique and powerful and that is something that really, no other program can hope to accomplish in a short time frame (sorry, Sublime Text).
That said, Vim hands down beats Emacs when it comes to pure text editing speed. It's keybindings are just a lot more powerful and flexible than Emacs's. And of course, that is what evil-mode is for. It emulates a subset of Vim in Emacs. It is by far the best simulation of Vim I have ever seen (judging from ViEmu, Viper, Vintage, Vico and Vimpulse), but it is not the real thing. Plus, there are lots of great Vim plugins that do not work in evil-mode.
I, for one, use Emacs and Evil and I am happy with it.
And I hope that Sublime Text will provide a potent entry-level drug for the next generation. But really, without open sourcing it at some point, I can't see it catching up to The Big Two.