My experience of the equation editor in Word on MacOS is that it definitely does
not support any meaningful degree of compatibility with TeX. Command-alt-E in Keynote works properly and seems to have most of amsmath imported by default: you can \begin{pmatrix} or \begin{cases} easily.
One of my worst weekly experiences is receiving documents in Word, especially papers written by colleagues with maths in them. Writing Markov chains in the supplementary methods section for a recent paper genuinely drove me to distraction; each non-ascii character was a major break from the flow of the sentence and requires a move to the mouse.
I really dislike Word in general, actually: on Linux (my workstation) LibreOffice is integrated well and polished; on MacOS it isn't as much as there's some value in having the 'real deal' product as administrators in my university use it a lot. I don't understand why Word's behaviour is interpreted differently from that of the rest of MacOS: e.g. in Word, clicking to select a chunk of text from the middle of the word automatically selects the whole word the cursor was in, unlike the rest of MacOS. This makes selecting parts of a word almost impossible, and it's not possible (AFAIK) to turn this behaviour off.