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.
I haven't noticed any performance issues in vim to start with. It was fast on a 75MHz pentium for me. The syntax highlighting, same. No issues. I don't always use that though because I can't be bothered to set up anything much past the basic config.
At one point vim lacked asynchronous plugins. If a plugin was running a builder or linter it locked the editor up (from what I recall).
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.
It was a real problem, but as GP already mentioned, Vim has integrated some version of it since Vim 8 (2016), probably at least somewhat motivated by NeoVim (forked 2014).
IIRC vim became really slow with the combination of large source files (thousands of lines of code) and language server plugins (e.g. code completion and live error squiggles).
Tree-sitter is more performant for sure, and its potential for easier text objects is nice. However, Vim's syntax engine is more than good enough for non-complex highlighting (and many people don't want complex highlighting) and, while I don't have enough tree-sitter knowledge to explain this myself, I've seen examples of Lua versions of Vim plugins where tree-sitter is unable to handle some of the regex-based text objects present in the vimscript version.
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.