REPL for Emacs Lisp

You'll have to be specific as to what you mean by "the rest". Except for the object inspector (that I"m aware of), emacs does all the above quite easily:

• editor (obvious)
• compiler - just run M-x compile and enter your compile command. From there on, you can just M-x compile and use the default. Emacs will capture C/C++ compiler errors (works best with GCC) and help you navigate to lines with warnings or errors.
• Debugging - similarly, when you want to debug, type M-x gdb and it will create a gdb buffer with special bindings
• Documentation Lookup - emacs has excellent CScope bindings for code navigation. For other documentation: Emacs also has a manpage reader, and for everything else, there's the web and books.
• version control - there are lots of Emacs bindings for various VCS backends (CVS, SCCS, RCS, SVN, GIT all come to mind)

Edit: I realize my answer about documentation lookup really pertained to code navigation. Here's some more to-the-point info:

• Looking up manpages, info manuals, and Elisp documentation from within emacs
• Looking up Python documentation from within Emacs.

Google searching will no doubt reveal further examples.

As the second link shows, looking up functions (and whatever) in other documentation can be done, even if not supported out of the box.

(the text below is my opinion, it should not be taken as fact or an insult)

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, organization, 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 recognizes 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