They're both text editors, but the similarity pretty much ends there. It may seem strange that two text editors could be so different. The key is that they're both specialized text editors, made for two very different tasks.
vim (or rather,
vi, which they imitate) were designed for writing e-mails and programs, respectively.
You're not meant to spend a lot of time in
nano: you go in, you type up your e-mail message (or whatever you were writing), and you get out quickly. Everything is based around getting you in and out as quickly as possible, so you can get back to whatever else you were doing. It goes so far as to list all the functionality at the bottom of the window, so you don't have to waste time looking up help screens. Of course, there's only so much room at the bottom of the window, and so functionality is constrained to whatever can be expressed, alongside all other functionality, in two lines of text. The result is extremely convenient for some things.
You're meant to spend much (if not almost all) of your time in
vim, so it tries to stay out of your way while helping you sling large chunks of text around quickly. A basic startup screen gives almost no information, and when you open a file you get only slightly more about where you are. And in both cases, you can't type text straight away: you start in "normal mode" and have to press
i to go into "insert mode" first (there are also a few other letters you can press instead of
i, offering some variations on this theme, and there are also some other modes I haven't mentioned). The learning curve is extremely steep: it comes with
vimtutor to help people out, but some people have gone so far as to write entire games dedicated solely to learning
vim's interface. Think about that for a second. An entire game, just to learn how to use a text editor. And people pay for it.
There is no question that
nano is better for the newcomer. I'm something of a
vim-zealot, and even I can't dispute that one. I've seen
vim turn newcomers off of Linux in general. And if you don't plan to do a lot of text-editing, or your text-editing tasks are all fairly light (like, say, writing e-mails), then
nano may be all you need.
That said, while mastering
vim takes a long time, the return on investment is high. I realize that the rest of this post sounds kind of down on
vim, but that's not my intent. You just need to know what you're getting into, because
vim is hard. But even its default configuration contains functions that automate a lot of common (and very repetitive) text-editing tasks: you can do with a few keystrokes things that could take many minutes, or even hours, if you had to do them all manually. There are plugins and scripts that take this even further. If you're going to be doing a lot of programming, or similarly long and involved tasks (dissertations, novels, etc), then
vim is ultimately the better choice, but you should still figure out
nano first: if an emergency comes up and you need to do something before you've figured out the basics of
vim, you'll want to be able to drop into something you're comfortable with.
Bottom line: start with
nano, and move to
nano gets tedious.