I have recently been awarded an individual postdoctoral fellowship (independent external funding for my own project) to join a research group at institution A. At the same time, I was applying for other postdoc positions, and finally I was offered a position by a professor at institution B. The group at B is more well-known and a slightly better fit for my research overall, but other than that the conditions (including salary and the institutions themselves) are similar. I cannot take the independent funding to institution B, so I have to choose between accepting the fellowship at A or a standard postdoc position at B.
Is having individual postdoctoral funding important enough to outweigh the disadvantage of being in a slightly worse group? I feel like having been awarded the fellowship is enough and I should choose the group that's a better fit for me, but people obsess over these named "prestigious" fellowships nowadays so I'm a bit worried that it'd be stupid to decline one and take a "regular" postdoc instead.