KaTeX does not support LaTeX commands like \label, \eqref, \notag, etc. As long as one does not need them, KaTeX is good. But if one needs them, MathJax becomes necessary.

I often do need these commands, especially while writing proofs, solutions, or long mathematical posts. See https://susam.net/blog/integrating-factor.html for an example. These commands make it convenient to refer to previous results using equation labels and numbers in long articles.

One can work around the missing support for these commands in KaTeX by writing their own HTML to simulate the same functionality but it is nice to have MathJax do this for us automatically.

Looks great, hadn't heard of KaTeX before.

Basic question: does it share any code in common with MathJax? If not, why not just run MathJax once server-side rather than on the client? Does MathJax have browser-specific accommodations, or does it not map to HTML at all, or is it something else?

Both MathJax and KaTeX let you run once server-side, if that's your fancy.

They map to a combination of HTML and MathML, with a bunch of CSS rules.

KaTeX's JavaScript code is a mere 68 KB when gzipped. IMO, that's worth it, so I don't have to fuss about with Node.js as much when generating the site.

Looks awesome, definitely giving it a try. Thanks!