I think the short answer is that we simply don't know yet which one is "better", especially since there are so many dimensions for what can make one vaccine better than the others:
- dosing schedule
- logistical constraints like refrigeration, shelf life
- rate of severe side effects (like allergic reactions)
- rate of mild side effects (like the severe cold symptoms I got from the J&J shot)
- duration of immunity
- effectiveness against emerging variants
- effectiveness at preventing hospitalization vs severe disease vs transmission vs infection altogether
We just don't have data to fairly compare the vaccines on all these dimensions.
The answer from a public health perspective is to get as many shots in as many arms as fast as possible, as long as they have low rates of severe side effects and are reasonably effective. However I agree that it sows distrust to not be honest & upfront about the fact that it's highly unlikely that all vaccines are actually equal, and that we simply don't have the data to know exactly how they differ. That could easily be followed up with a "once we figure out which ones are actually better we'll give additional vaccines and/or booster shots to those that drew the short straw".
Pretending they are all equal is only going to further erode trust when we inevitably figure out how they're not actually equal.