I think a major difference is that you are not forced to take the Flu Vaccine. "Anti-Vaxes" just want to be able to make a choice. Also, the flu vaccine has been already for years, unlike these new vaccines which the long term side-effects are completely unknown and they use completely new technology.
From personal experience, 5 years ago I stopped taking the flu vaccine and I had been taking it for years and ever since I stopped I haven't had the flu once... When I had the flu vaccine, I would always get sick the next day and sometimes I would get it sick again a few weeks later.