The reason why you saw the latter post is probably because there's a new CDC study (published on Oct 29) with results pretty contrary to the earlier Israeli (Maccabi) study.
CDC used data from the VISION Network* to examine hospitalizations in adults with COVID-19–like illness and compared the odds of receiving a positive SARS-CoV-2 test result, and thus having laboratory-confirmed COVID-19, between unvaccinated patients with a previous SARS-CoV-2 infection occurring 90–179 days before COVID-19–like illness hospitalization, and patients who were fully vaccinated with an mRNA COVID-19 vaccine 90–179 days before hospitalization with no previous documented SARS-CoV-2 infection. Hospitalized adults aged ≥18 years with COVID-19–like illness were included if they had received testing at least twice: once associated with a COVID-19–like illness hospitalization during January–September 2021 and at least once earlier (since February 1, 2020, and ≥14 days before that hospitalization). Among COVID-19–like illness hospitalizations in persons whose previous infection or vaccination occurred 90–179 days earlier, the odds of laboratory-confirmed COVID-19 (adjusted for sociodemographic and health characteristics) among unvaccinated, previously infected adults were higher than the odds among fully vaccinated recipients of an mRNA COVID-19 vaccine with no previous documented infection (adjusted odds ratio [aOR] = 5.49; 95% confidence interval [CI] = 2.75–10.99). These findings suggest that among hospitalized adults with COVID-19–like illness whose previous infection or vaccination occurred 90–179 days earlier, vaccine-induced immunity was more protective than infection-induced immunity against laboratory-confirmed COVID-19. [...]
Secondary analyses that did not adjust for time since infection or vaccination or adjusted time since infection or vaccination differently as well as before and during Delta variant predominance produced similar results.
The most baffling part about this is that both the CDC and the Israeli study used fairly similar designs; here's relevant bit for the Israeli one:
In model 1, we examined natural immunity and vaccine-induced immunity by
comparing the likelihood of SARS-CoV-2-related outcomes between previously
infected individuals who have never been vaccinated and fully vaccinated SARSCoV-
2-naïve individuals. These groups were matched in a 1:1 ratio by age, sex, GSA
and time of first event. The first event (the preliminary exposure) was either the time
of administration of the second dose of the vaccine or the time of documented
infection with SARS-CoV-2 (a positive RT-PCR test result), both occurring between
January 1, 2021 and February 28, 2021. Thereby, we matched the “immune
activation” time of both groups, examining the long-term protection conferred when
vaccination or infection occurred within the same time period. The three-month
interval between the first event and the second event was implemented in order to
capture reinfections (as opposed to prolonged viral shedding) by following the 90-day
guideline of the CDC. [...]
After adjusting for comorbidities, we found a
statistically significant 13.06-fold (95% CI, 8.08 to 21.11) increased risk for
breakthrough infection as opposed to reinfection (P<0.001). [...]
After adjusting for comorbidities, we found a
27.02-fold risk (95% CI, 12.7 to 57.5) for symptomatic breakthrough infection as
opposed to symptomatic reinfection (P<0.001). None of the covariates
were significant, except for age >=60 years.
The CDC's study actually offers a two-pronged theory why the results were (so) different:
The Israeli cohort study assessed any positive SARS-CoV-2 test result, whereas this study examined laboratory-confirmed COVID-19 among hospitalized patients. The Israeli cohort study also only examined vaccinations that had occurred 6 months earlier, so the benefit of more recent vaccination was not examined.
Also, since the Israeli study didn't rely on a "captive" population that ended up in a hospital, it's possible that participants' choice to [not] get tested might have influenced their results.
Natalie Dean, a biostatistician at Emory University, adds: “The biggest limitation in the [Israeli] study is that testing [for SARS-CoV-2 infection] is still a voluntary thing—it’s not part of the study design.” That means, she says, that comparisons could be confounded if, for example, previously infected people who developed mild symptoms were less likely to get tested than vaccinated people, perhaps because they think they are immune.
The CDC's study also points out potential problems like that in their own study design:
selection bias might be possible if vaccination status influences likelihood of testing [by the hospital] and if previous infection influences the likelihood of vaccination. Previous work from the VISION network did not identify systematic bias in testing by vaccination status, based on data through May 2021. [... R]esidual confounding might exist because the study did not measure or adjust for behavioral differences between the comparison groups that could modify the risk of the outcome. [... T]hese results might not be generalizable to nonhospitalized patients who have different access to medical care or different health care–seeking behaviors.
Another element of difference between these studies is that the Israeli one only includes the Pfizer vaccine, while the CDC one has both Moderna and Pfizer pooled (J&J was excluded). Unlike in the clinical trials which showed these two mRNA vaccines to be similar, in more massive US retrospective studies such as one done by the VA (on 620,000 participants), Moderna was superior to Pfizer, both initially and its effect decayed less over time, but the difference is nowhere near enough to explain the reversal in results in the CDC study relative to the Israeli study.
I suspect the last word on this (which exposure source provides broader/better protections) hasn't been written.