> While, an infection produces fewer antibodies, relatively speaking of course, but they last longer. Yes?
Antibodies are antibodies. They're all subject to the same fundamental breakdown and clearance mechanisms in the body, and don't really "last longer" based on origin. There's a dosing effect (i.e. a big spike lingers longer than a small one), but the dynamics of the process don't change, so far as we know.
As an aside, all of these arguments based on antibody levels/neutralizing titer are extremely reductionist, and we have plenty of clinical data now that is better and more to the point. The immune system is more than antibodies. This debate is pretty facile.
It's perhaps interesting to talk about neutralizing ability of antibodies "natural" vs. "vaccine" if you're interested in making a better vaccine, but even then, there are so many versions of "natural" immunity that any general discussion is pointless. Everyone has a different antibody response, and moreover, antibodies are targeted to whatever variant(s) you've seen in the past. Meanwhile, there's exactly one vaccine variant. Broad comparisons are almost impossible.