Elvis is a superset of vi. It runs on more operating systems than vi, it is free, and you can obtain the source code. Elvis also has many new features. These new features are described in the first chapter of the online manual, which hypertext links to the other parts of the manual where those features are described in detail. Here's a just brief list:

Multiple edit buffers, so you can edit several files at once.
Multiple windows, so you can see multiple edit buffers, or different parts of the same edit buffer.
Multiple user interfaces, including graphical interfaces under Windows95/98/NT and X11.
A variety of display modes, including syntax coloring and HTML.
Online help, with hypertext links.
Enhanced tags, to support overloading in C++.
Network support, so you can load/save files via FTP, or even use elvis as a light-weight Web browser.
Aliases, which allow you to define new ex commands.
Built-in calculator