Possibly, though positive Covid tests aren’t a guarantee of an actual infection which might be why some studies showed vaccination was more effective.

Alternatively, having survived the first infection says more about the individual than getting a vaccination. Which is yet another way this stuff gets tricky.

> some studies showed vaccination was more effective

Could you point me to them? I'm unable to find any.

Here’s one showing prior infections or at least prior positive test results failing to result in long term immunity.

https://wwwnc.cdc.gov/eid/article/27/9/21-1042_article

The linked article does not study long term reinfection rates, it studies systemic antibody response. Unfortunately, the topic of long-term covid antibody research is a difficult area: both exponential antibody decay and antibody location are relevant. Extrapolating epidemiological conclusions from small population antibody studies is reaching.

Population studies run into different issues you want both. I recall an early study showing vaccination being significantly more effective, but that’s before current variants showed up etc.

Really you can’t draw accurate conclusions from any one study but multiple studies give you a better picture of what’s going on. Large numbers of people falsely believe they had COVID, people who survived COVID are healthier than the general population because the other option is death, the most common infection doesn’t get a strong immune response, vaccine recipients tend to be older and in worse health etc.

That said, an otherwise healthy person who got very sick from COVID and got multiple high quality tests verifying exposure likely does have a significantly better long term protection. But, that’s not representative of the general population that had COVID.