Each is a tool that has it's uses. There are things that emacs does better, and things that vim does better. Knowing both is a good thing. I develop software for a living, and use both on a daily basis.
Vim is pretty easy to get started with. Learning about 10 commands will let you do 95% of what you want to do. Emacs has a steeper learning curve, but IMHO gives more control for more complicated tasks.
If you're planning on doing any sysadmin type work, learn vim. It's great over a slow connection, and is pretty much guaranteed to be installed on any unix system you encounter.
Then go learn emacs.