Neovim can basically do everything Vim can with one major advantage - the number of contributors to the code base is just so much wider (Vim is ~100% maintained only by B. Mooleanaar). Whatever you learn for Neovim you can also apply to Vim and vice versa. And of course there is the never ending Vim vs Emacs controversy - but better not get into that war.
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For web development definitely NeoVim. It supports more plugins, especially themes. Vim is more for scripting and server related stuff, it is more raw. NeoVim is literally described by it's name..