No, infection is not more protective than vaccination. Vaccination is much more consistent than infection - not least because the vaccine is not packaged with immune suppressing elements.
https://www.nature.com/articles/s41598-022-05325-5
There are other studies that say the same thing - natural immunity is far superior to vaccination. (But also more risky since acquiring that immunity can cause people to end up in the hospital.)
The best is both:
"Two doses of BNT162b2 vaccine were associated with high short-term protection against SARS-CoV-2 infection; this protection waned considerably after 6 months. Infection-acquired immunity boosted with vaccination remained high more than 1 year after infection." https://www.nejm.org/doi/full/10.1056/NEJMoa2118691
Please provide sources for your other studies - "far superior" is quite a strong claim
"A total of 6169 participants in the previously infected cohort were followed in the unvaccinated follow-up period and up to 1 year after a primary infection. These participants were predominantly infected in the spring of 2020 and were followed in the period before emergence of the delta (B.1.617.2) variant."
C'mon buddy, do better!