If you look in more detail at the Pfizer vaccine and several of the others under development are mRNA vaccines, which are new, there has never been a mRNA vaccine released to the general public, just some experimental vaccines using mRNA technology in the last few years, so the long term potential complications from this class of vaccine is unknown. Also one of the big challenges of mRNA vaccines is that they must he stored and transported at very low cryogenic temperatures (-94F), which means there will be distribution challenges, as these can't just sit in the refrigerator at the pharmacy or doctors office waiting to be used (refrigerator storage shelf life is under 24 hours). So expect large public assembly line injection stations being set up to give doses at scheduled times.
Other vaccines are under development using more traditional vaccine production which does not require cryogenic transport. This is not to say which is safer, just saying the challenges and the unknowns are higher with the mRNA vaccines.