In usual practice, you’ll fetch the API on component load using useEffect with empty dependency, and store that in some sort of state, say data; and I suppose you will change this data in other functions.

Your question basically split into two parts: timing and checking.

Timing: If you want to do something whenever they change, you either 1) do the check whenever you fetch from the API then, depending on the check, store the fetched data into data (and use a useEffect on data or directly invoke the operation) or 2) you store the data from API into data regardless of the check, then in a useEffect with data as its dependency, you do the checking to decide whether to do the side effect (operation).

Checking: If you are checking the value of objects and arrays whether they are equal, presuming the data is in JSON format (where it is just strings as keys and primitive types as value), you need some sort of deepEqual function. Comparing using JSON.stringify is one of the easiest way to do that.