Emacs vs Vim is more a matter of personal taste.
I have used both, here are my opinions.
Note: I was a vim user that switched to emacs.
Vi/Vim:
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It IS worth learning because it is the de-facto standard editor on most unix and unix-like systems, and most of the times it comes preinstalled. The basics can be learnt in half an hour or so.
The nice thing about vim is that it fits very well in the Unix environment doing basically one thing and doing it fairly well.
Please note that vi and vim are two different things: 'vi' is more of a family of editors, with vim being the most widely used one. Most vi-like editors share the same keybinding and stuff, and you can use most using the same of keybindings and concepts.
One of the things where vim falls short is that its scripting language is quite crappy, and it's quite a PITA to work with. Plus once you learn it, it is quite useless outside vim.
GNU Emacs
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GNU Emacs is a radically different approach to editing text and it resembles one of the early lisp machines: you have a bunch of functions lying around and you call and compose them as you need them.
The learning curve is quite steep but it is very flexible, it has a reasonably nice scripting language that you can use even outside (well, most of the syntax).
The thing I like about emacs is that it gives you a coherent environment to do most of your things, and a scripting language to customize most of its aspect.
So what?
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Well, nothing. Try them both and stick with what you like.
I think it is really worth to learn at least the basics of both.
To be fairly honest, I have some pain points with both of them... But that would be OT, and better suited for another post :)