Both Vim and Neovim work fantastically. However, I'm personally using Neovim because I want to support its philosophy and goals. I like the Neovim team's approach to project management and am excited by their ambitious vision, which has already led to an embedded terminal and async stuff (yes, Vim now has these as well; perhaps they're influencing each other). The maintainer (Justin Keyes) and the contributors are doing amazing work.
Since it has a cleanly separated UI, Neovim can be embedded anywhere. I'm looking forward to the day when I can compose Reddit posts in Neovim right inside the browser's input box! Neovim, in part, is the promise of using Vim anywhere you can type text: Gmail, Twitter, etc. And by Vim I mean the real thing (with your configuration), not some half-baked emulation supporting a subset of the keybindings.