There is no need to change the newer Mac if all you need is the files from the older Mac.
Migration Assistant is the software to use.
Move your content to a new Mac - Apple Support
If I were King, I would entitle that article "COPY your content to a new Mac". It is not actually MOVED (the old is NOT deleted).
-------
If you wish to have all your Account information and settings and passwords copied and usable as well, You will need to work harder at making the new(er) Mac pristine, and FoxFifth's article will do just that for you.
Then Use Setup Assistant (runs by default at first run) to Copy all your pre-existing information from your old Mac, rather than set up as new.. NB>>This is the easiest way to retain your passwords and settings.