The short answer: if you're happy with your productivity in Emacs, then there's likely no compelling reason for you to switch, unless you enjoy the challenge of learning a new text editor.
Speaking as a longtime vim user, not if you already grok Emacs. The one really good reason I can think of is that vi is pretty much ubiquitous on *nix and might be better suited if you need a powerful editor which you can almost always expect to be there for you even over ssh.
I have not used Emacs, but Vim feels incredibly powerful to me. I feel that I can tell it what to do in a very natural way: "change inside parentheses", or "delete from here to the word 'foo'," or "replace 'bar' with 'baz' inside the current set of curly braces."
Most of my time in code is spent moving around, editing and refactoring. Vim fits that: "Normal" mode puts an entire keyboard of commands at my disposal for for moving around and editing - no need to press Control or something to say "watch out, I'm going to issue a command!" Of course I am - that's what I mainly do. If I actually want to type, I go into insert mode.
I have written the beginnings of a book to explain the power of Vim, if you'd like to check it out. I'd love any feedback anyone wants to give.
You should learn VIM for the same reasons a Haskell programmer should learn Common Lisp. Not because you don't already have an extremely powerful tool. Just because there are other extremely powerful tools and the perspective is worth it.
My experience is this: Emacs has better integration to tools (like debuggers, etc).
However, I like the Vim input model, where you combine commands (like delete or yank) to a motion (like a word, 3 words or everything inside these parentheses).
Emacs has the Viper mode, which gives basic Vi-style input model but it doesn't do advanced stuff like text objects.
IMO any serious coder should try both, Vim and Emacs and see which one works better.
I have next to no experience with Emacs so from the perspective of a 'normal' text-editor-using-guy Vim is (Warning, some slight exaggeration ahead) one of the greatest things I have discovered, learnt and now use daily.
Why? I can do simple things faster (Delete a single char, delete a line, search/replace, etc.), it seems like a more logical way to write, and so on.
I assume it's because your original question, vi/vim vs. emacs is a decades old flamebait question, and it probably seems unlikely to some people that anyone could become a proficient emacs user and end up on Hacker News without ever encountering at least the jokes about vim vs emacs holy wars.
I increasingly see posts on HN about vim, rather than emacs. I like emacs, but wonder whether it's worth trying to use vim instead of emacs. I honestly couldn't give a damn whether some nerds like to get their knickers in a twist re. which editor is best.
The short answer: if you're happy with your productivity in Emacs, then there's likely no compelling reason for you to switch, unless you enjoy the challenge of learning a new text editor.