As Derek Elkins says, MathJax is rendered client-side both here and on StackExchanges.
That means that Internet connection speed as well as server latency only influence how long it takes until the content is loaded and your browser starts rendering.
It seems that the used scripts are currently
https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML-full for StackExchange and
https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js for Codidact.
Maybe there are also specific settings of these libraries that can influence the rendering speed.
Just now I compared the rendering of a simple matrix with about 20 rows pasting it into the ask question form of math.stackexchange/codidact and waiting for the preview to render and while StackExchange was almost instantaneous, Codidact took like half a second to start rendering but didn't take longer, when I increased the number of rows in the matrix. I therefore guess that the delay for Codidact is simply a delay to not constantly update the preview form while StackExchange doesn't do that (I didn't want to publish dummy questions).
Overall I very much expect the pure rendering performance of MathJax to be quite similar on both platforms. One would need more sophisticated setups to really measure it.