If anything I can see confirmations that natural COVID-19 immunity is on par with COVID-19 vaccines with a lot of outside factors that can influence outcomes in either side.
However, it seems that immune system is very complex and does not work with only antibodies. Even though Natural ~ Pfizer on KPIs these studies usually measure, there are other mechanisms like T-Cell immunity, which are most definitely trained during actual disease, but which might not be activated by narrowly focused vaccines and are hard to measure so we don't know how they work on the wide scale.
For example here[0], blood plasma seems to be different between natural vs vaccinated.
At the same time this rhetoric undermines credibility of institutions and individuals that project such ideas. It seems that in one case the approach is strictly rational and in another we turn our eyes at facts and don't want to believe that our bodies are able to produce something better then scientist at Big Pharma.
People who got COVID-19 already lost in this global roulette game since they are the ones that already absorbed the highest risk in this game. The upper side of it is that if you got out the other way - you get better overall immunity for further reinfections. And now authorities want to push them even further, take even more risk(minimal, but still) which is not necessary based on what data says.
[0] https://www.fda.gov/media/136798/download#page=10
P.S. sorry for rant.