Don't forget Covid/SARS-Cov-2 is only 6 months older than the vaccines: Nov-2019 vs Apr-2020.
Every bit of data that we have today about the safety profile of the vaccines vs Covid indicates that for the majority of people vaccines are orders of magnitude (think 100-10000x) safer than Covid.
Even when they aren't, e.g. children or AZ & young women, we are talking about super small risks similar to an average car ride.