Way more infectious that the vaccine, though, and probably not any more effective. Nobody's caught the vaccine from the exposure that I've seen mentioned.
It seems like you're under a misapprehension that there is some mutually exclusive tradeoff of "vaccine vs infection" to be made, but this is not the case. It's well established now that natural immunity is more effective and longer lasting than the vaccines. And again there's no point in the infectivity comparison because whether someone is vaccinated or not makes no difference to their odds of contracting or spreading Covid -- if anything, the current level of case rates in highly vaccinated countries vs less vaccinated ones suggests the vaccines have made infection more likely.