as a textmate to vim to emacs user, I'd say that vim is to textmate as emacs is to vim. Vim is awesome, but it's still just an editor. Emacs is an operating system that's built around editing text. You start with a powerful editing paradigm and then apply it to pretty much anything you need to do as a programmer...it's about the best editing experience I've ever had. My shell, source control, organiser, messaging, documentation, directory browsing, irc, document viewing etc is all done from within my text editor with all the awesome editing capability that 23 versions brings with it...also you can run vim from within emacs...
Exactly. Emacs didn't start on Unix IIRC and seems to prefer to have everything built in. vi was created by Bill Joy on Unix and wanted to work with the rich language of shell commands from the start, as ed(1) did, so it concentrated on editing text well and integrating with Unix well. To see some Emacs users you wonder why they're even bothering to run on Unix. ;-)
