Yes, in point of fact, they are better than vi/vim because they are non-modal. When all is said and done, dropping vi's modes makes an editor better and more efficient.
> Like delete the next four words? How do I do that in a modern editor with a single keystroke?
You can't delete four words with a single keystroke. You can delete [N] words, but only after switching modes and choosing the desired number.
Source: http://www.lagmonster.org/docs/vi2.html#delete
Quote: "ndw : Deletes the next n words starting with current"
The above assumes you're already switched to the required mode, so a minimum of four keystrokes if the number [N] is a single digit. Then, to continue typing, you have to switch back to the mode you started from. Total five keystrokes minimum.
> In the end, two things sealed the deal for VIM for me. 1) it's on every remote server I have to access, and 2) I've put the time into it, so I'm quite efficient in it.
This is circular reasoning. The reason vi or vim is out there on all those servers is because of the number of people who haven't learned anything else.