I used neovim because it felt way faster by default. I think treesitter runs circles around what classic vim is using to highlight syntax. That said, I never used both beyond basics, thus no horror stories either.
That fell apart when people wanted vim to do some more modern IDE kind of things like all the “… on save” stuff (build on save, test, lint, etc). I think LSP support is native in neovim as well.
I believe vim merged asynchronous plugin support a while back though, so I’m not sure how different they really are anymore.
Just run make from another terminal...
I often use vim or nvim on disposable machines, so persistent undo is something very low on my list of things I want.
As far as really cool uses for tree-sitter go, ast-grep is a fantastic tool. Of course it's a standalone program, so it doesn't need nvim to make use of it.