I normally use a higher end hex editor. Hex workshop has a file compare, even a resyncing compare if you need that. Not sure what we are pointing people at as far as free software right now.
https://www.guiffy.com/Binary-Diff-Tool.html was high up in a search though and apparently available for free. Most of the time you can do things for free but where a fancy editor is all in one you might have to combine the efforts of a few programs, old but still accurate enough
https://gbatemp.net/threads/rom-hacking-hex-editors-mid-2012-discussion.326873/ .
For search times file compare, binary compare, possibly diff and binary diff (as in difference) but you might also get patches/patch making for that one which is less useful (well technically it is very useful but you would then be lumped with figuring out the patch format so best go with a nice GUI tool).
There are some things that might get in the way. Pokemon for instance quite famously cycles between a few spots, partially to avoid writing the same bit all the time and partially so you can have the backup of however long back it was.
Anyway assuming you have an easy route (or can work around it -- figuring out where the saves land is one thing, saving twice to land back on the same spot if it is just the two things cycled between is another) then depending upon what is in the game there will likely be two or three areas that change.
1) The checksum area. If something changes then the checksum changes.
2) Any gameplay time, step counters, save counters and whatever else goes up just for being saved or in the game.
3) The data you want to know about.
Easiest way to eliminate 1) and 2) is save, dump the save, save again and compare. As you changed nothing else then whatever changes when you actually change what you want (harder for names/strings, easier for things like potions or money),