With Emacs you are expected to have it open 24/7 and live inside the program, almost everything you do can be done from there. You write your own extensions, use it for note taking, organisation, games, programming, shell access, file access, listening to music, web browsing. It takes weeks and weeks till you will be happy with it and then you will learn new stuff all the time. You will be annoyed when you don't have access to it and constantly change your config. You won't be able to use other peoples emacs versions easily and it won't just be installed. It uses Lisp, which is great. You can make it into anything you want it to be. (anything, at all)
With vim, it's almost always pre-installed. It's fast. You open up a file do a quick edit and then quit. You can work with the basic setup if you are on someone else's machine. It's not quite so editable; but it's still far better than most text editors. It recognises that most of the time you are reading/editing not typing and makes that portion faster. You don't suffer from emacs pinkie. It's not so infuriating. It's easier to learn.
Even though I use Emacs all day every day (and love it) unless you intend to spend a lot of time in the program you choose I would pick vim
2.
Vim:
- better as an editor
- more active scripting community - internal language: vimscript
- one central repository of scripts, plugins, color schemes, ...
- also extensible in python, ruby
- can be made portable (emacs has some problems with that)
Emacs:
- non modal (most of today's editors have taken this approach)
- more powerful language for extending it (elisp is a full blown language, and in emacs you can practically redefine everything; while in vim you cannot redefine build in functions of the editor. On the downside, vimscript is relatively similar to today's dynamic languages while elisp doesn't resemble pretty much anything)
- more extendible
- excellent support for GNU tools (the bunch of them)
Personally, I prefer vim - it is small, does what it's supposed to do, and when I wish a full blown IDE I open VS. Emacs's approach of being an editor which wants to be an IDE (or should I say, an OS), but is not quite, is IMHO, outdated. In the old days having a email client, ftp client, tetris, ... whatnot in one package (emacs) made some sense ... nowadays, it doesn't anymore.
Both are however a topic of religious discussions among the programmer and superuser community users, and in that respect, both are excellent for starting flame wars if put in contact (in the same sentence / question).