MathJax lets you select text more often than KaTeX as far as I can tell (some KaTeX formulas act dead unless you start selecting outside them), not that either library give you anything especially useful if you try to copy and paste. MathJax will happily give you useful copy-to-clipboard if you right click.

MathJax has way more accessibility features: https://docs.mathjax.org/en/latest/basic/accessibility.html