Some things that Mathjax can do that I believe Mathquil cannot (likely some are possible in Mathquill)
3. Macro Map
4. Strikethrough for canceling equations
5. Automatic line breaks
6. Aligned, flalign, gathered environments and \\[# pt] for custom space between lines
7. Colored bounding box and colorbox for part of an equation
8. Give part of an equation a CSS class
9. \displaystyle for in line equations
10. \hspace, rule
11. Equation numbering
12. Coloring only part of an equation text
13. The Mathjax Google Groups where I can ask complicated questions and get answers for them
14. Limit with arrow underneath in text in front of it.
15. Genfrac (custom fraction bar width and space before and after fraction bar)
16. Underbrace and Overbrace
17. Begin cases (piecewise function)
18. Inline equations being bottom aligned with text instead of top-aligned
I'm interested to see which of these are possible in Mathquill let me know.
The Mathjax react.js examples require the user to type in the latex, unlike Mathquill where the user types within the rendered math itself.
I wonder if it would be easier to add the missing features to Mathquill or add the Mathquill textbox behavior to Mathjax. I'd like to hear some opinions on this (I will attempt to hire someone to add the missing features either way).