Both have terminal and gui interfaces. The main difference (by default) is that vim has a mode for moving around and a mode for entering text and emacs does both at the same time (mostly by holding ctrl for moving around), but both can be configured out the wazoo to do either to some degree.
The joke that resonates most with me is: "Emacs can do anything - it's easily one of the most configuration programs ever created, and is practically its own operating system. Unfortunately, it doesn't come with a decent text editor"
In all seriousness, I don't think anyone really takes these things to heart anymore. I picked up Vi because it was on all the systems that I use. Once I began to learn it, i moved to Vim, as most people do. Later, Neovim got to the point that it was a drop-in replacement for me, seemed to be a more viable path for long-term growth given its focus on refactoring the core codebase and explicitly dropping legacy support for some features to that end, and early focus on speed through concurrency.
I'll grouse with emacs users a bit, but honestly... I can't open Vi on someone else's machine and immediately be useful, either. There isn't a huge difference in learning curve for me between "Vi configured by someone else" and "Emacs".
As a long time Vim user (oh gosh 18 years already!), to me the Vim vs. Emacs war has always been a lighthearted joke. If there's any real war, it's more between text editors and IDEs.
I've been "attacked" on several occasions by IDE users for using Vim. Not once by an emacs user.
