Vaccine-based immunity certificates have less scientific uncertainty associated as the pattern and efficacy of immunity conferred by vaccines will have been measured during the vaccine trials across a diverse range of people. Also, vaccines provide a consistent stimulus of immunity (within a given vaccine) so less uncertainty than natural immunity generated through an illness of variable severity.
They also have significantly less moral hazard associated with them, as receiving a vaccine is a pro-social activity, compared to deliberately seeking out infection (a decidedly anti-social, damaging to public health activity) incentivised by natural antibody based immunity certificates.
However, there are still concerns about the efficacy of vaccines. A vaccine that is 50% efficacious would mean that half of those with the vaccine could still be at-risk and a risk to others. Middling efficacy is fine at population-level when the goal is to bring down R below 1 consistently across the population but could be problematic in certifying any given individual as 'safe'. Also, a number of different vaccines with differing efficacies (potentially differentially efficacious across different demographic groups) will be available. Some efficacy threshold will likely need to be determined for any vaccine-based immunity certificate (perhaps with different thresholds for different activities based on their respective risk), with potentially personalised risk scores even for those having had the same vaccine.
There are also significant questions of unequal access, given the limited capacity of vaccine production and distributions, which suggests there may not be sufficient vaccines for the whole world for multiple years, which may made even worse if there is the need for booster doses of vaccines or even an entirely new vaccine for a sufficiently mutated strain of COVID-19.