Which features are complementary? Pretty much everything that isn't straight text editing. Reading mail, usenet, running a shell, debugger (gdb), compiling, version control integration, man pages, todo lists/project planning (org, planner), browsing web, ide (CEDET), IM, IRC, remote file editing (TRAMP), etc. There are even silly things like games: tetris, snake, bubbles, pong.
Within the domain of strict text editing, both Emacs and vi do the job, which you prefer is like which ice cream you prefer. And I agree with richardhoskins, Viper mode is probably the way to explore Emacs if you're not interested in switching whole-hog.
Note: Apologies if any of the features are provided in vim, it's been a long time since I used it, and I was a very simple user of vim.
Best Answer
Google for "emacs for vi users" The first 3 links are all tutorials which will do this for you.
http://www.elmindreda.org/emacs.html
http://grok2.tripod.com/
http://bradbeveridge.wordpress.com/2007/06/21/how-a-vim-user-converts-to-emacs/
etc etc.