A tool like this was at the core of the Twitter frontend rewrite done years ago ~2011 time frame. Diffed both HTML and JSON responses, at scale, to find any issues. Amusingly found lots of issues in the original where the new system was correct.

edit:

We did it via a front-end proxy that would send the request to the original system, get the response and send it, then send the request to the test system along with the response from the first system and diffed them. Had a bunch of heuristics for various element types where you could expect differences between them (timestamps mostly).