It will be hard to know for sure. Vaccines, even mRNA, adjust two components: memory cells and anti-bodies. Anti-bodies are short lived (6 monhts in case of COVID) and act fast when the treat re-emerges. Memory cells are slower, but last your whole life time. In theory, just a single injection builds up enough memory cells to change how your body react to Covid-like viruses. Same if you get infected. You would need a much bigger viral load to take you to the ER.

Since billions of people took the vaccine, multiple times, plus millions of people got infected, this exposure could have had a massive impact on visits to the ER and further deaths because of ER overcrowding. What we know for sure is that the ER usage due to COVID significantly dropped over time. That could have been the vaccines, infections, virus getting weaker, etc. But in the end, we will never know. And the comparison you made doesn't take that unkown into account.