No - we do not have "every reason" to expect, quite the opposite. As a starter, for many infectious diseases (incl. viral diseases) vaccine-induced immunity is better, see e.g. the commentary and examples here [1].
Regarding SARS-CoV-2, the picture is a lot more subtle. Directly from German virologist Christian Drosten:
"If you look closely at the data in the studies, the situation is much more complicated. What one should say and be aware of is vaccination, which provides a relatively constant protection, which is very well described in studies. You actually pretty much know what you have. While there is a greater spread in the case of infection. Quite simply, we get different amounts of virus in the infection. Some have a silent infection that they don't even notice, others have a symptomatic infection. And you have to be aware that in such studies, which are primarily based on PCR test results, there will always be a certain emphasis on symptomatic courses. That means saying that if I know I have survived an infection and it was confirmed by PCR testing, then that also implies that I had symptoms, otherwise I would hardly have had a PCR test at the time. So then I had a symptomatic course. I think that for this situation you can now say very well, whoever had the whole thing symptomatically, will be well protected afterwards, almost like a vaccination." [2]
The study you picked in its current pre-print form does not adequately address this obvious selection bias, nor does it address the inherent survivorship bias. I´m not a medical expert though, so we will see if it passes peer review.
In any case, please do not perpetuate the myth that natural immunity is superior per se. If you had a symptomatic infection plus a PCR test, you are likely well protected, very similar to (mRNA) vaccination. If your infection is more than 6 months old, get a booster.
[1] https://twitter.com/ENirenberg/status/1412865782862725125
[2] https://www.ndr.de/nachrichten/info/coronaskript334.pdf page 7 (via Google Translate)