I may have not understood your original post correctly. If I did not, mea culpa.
I took your post (as did @hass5744) to mean you are using the radio/tv audio to ascertain the performance of two sets of hearing aids for your hearing in general, that is, extrapolating from this comparison to other listening situations. If that is your meaning, this comparison does not transfer to other situations, no more than e.g., a listening in quiet test is of any use when testing performance for speech in noise. Each environment has its differences, and so the user needs to prioritize those environments and then subjectively evaluate each HAās performance in each. If it is easier to use some sort of ad-hoc scoring system of your own creation to record the results of each test, thatās fine although for most people just taking notes is sufficient (and probably most folks donāt even do that, no doubt contributing to the low success rate). There is no objective measurement tool for this purpose, because hearing is entirely subjective. Take a minute to write down the listening environments you are in 90% of your time. The list is probably not all that long; far, far less than āhundredsā. Identify whatās most important (e.g., a spouseās voice, your place of work, etc.) and focus on these. You will find that a small number of environs constitute a large majority of your usage.
Where it becomes particularly challenging is when the HAās come from different providers or the HAās are not programmed to the same target or an insufficient amount of trial time is allotted. These factors can compromise comparisons. Again, there is no objective measurement system to get around this. Itās a matter of you understanding the process and working to ensure comparisons are consistent as much as possible. This is one reason that you see so many here emphasizing the importance of finding a very good audiologist who can cooperatively guide you through the process. The audiologist starts with your audiogram and then will fine tune the instruments based upon your subjective feedback, just as optometrists or medical doctors do all the time. The patient and the provider are making judgment calls. This process while based on science, also involves a good bit of art on the part of the provider.
But if what you are asking about is just how to make a radio/tv comparison specifically, well, the answer is essentially the same as it is for any other use case, per the above. Ensure that your test is consistently the same, and ensure that the HA solution is consistent (e.g., a music program added by the audiologist to each set of HAās, customized to your hearing loss). Your subjective experience is the test output.
As an engineer, I worked with objective technical measurement systems all the time as well as clientās subjective evaluations of technology, too. No different with HAās. Start with the former (the audiogram, etc.), proceed to latter (fine-tuning against your identified test cases).
HTH.