Are you willing to get the Covid vaccine when offered?

Furthermore, I'd imagine that ethically, we can't run a real controlled test. You can't put 1 infected, coughing person in a room with 100 other people. 50 vaccinated, 50 not. And see who does and doesn't catch it and/or die.

It would be manslaughter or reckless endangerment or something.....

So, the aggregate numbers are going to always suffer from behavior. Do vaccinated people take more or less precautions than unvaccinated? It depends, but I bet on the average many vaccinated still are keeping relative distance from others and still using a mask, depending on the situation.
Totally agree, there is no ethical way to efficiently determine this, that I know of. Using a species that contracts and spreads the virus in a similar manner would be the way to go. Maybe non-human primates, but that gets super expensive super fast, especially at the numbers required.

And just because person A and person B both came down with covid at some point doesn't mean their future immune responses will be equal. There just isn't an efficient way to test this. The antibody test only sees a threshold of detection (either you have the antibodies or you don't), it doesn't measure their entire immune complement response to determine a future prognosis.