What we've seen in the US is that the J&J was the choice of people who legitimately wanted a vaccine but were leery of the novelty of the mRNA vaccines. This is going to crush that group of candidates and some non-zero number of them will wind up in the camp of people who don't get vaccinated at all.

What you will find is that the vaccine-hesitant are perfectly happy to take the word of authorities who say "this vaccine is unsafe" and only have trouble accepting the word of authorities who say "this vaccine is safe".

I think that is likely because the two states have different levels of confidence, similar to how "not guilty" is not the same state as "innocent". It is relatively easy to identify unsafe, especially when negative effects arise quickly. It is harder to reliably determine safe as it may just be a matter of time before negative effects arise.

For people who won't accept the vaccine regardless, it doesn't matter either way. For people who can be convinced, I think that obvious evidence of caution may be helpful in convincing them.