I agree with the above posters that it definitely in the end boils down to how you treat the patients.
HOWEVER, I will say that given the choice for fellowship, all else being equal, it is a smart idea to choose the one that has better name recognition with the general public. You would be surprised how many patients have blind trust in you because you have harvard or yale or stanford on your resume vs Bascom Palmer which a lot of patients havent heard of, simply because of the name recognition. I have had patients switch their care to me simply because of this.
I feel like overall patients like
1) local guys and girls (aka trained in the location they are practicing) because they know the universities and hospitals in the area and their own families have been treated at places you trained
2) training with name recognition if you dont plan on staying where you trained
But I think overall, you go where you think you will get the best exposure to pathology, can form the closest bond with your mentors (believe me, you will have a LOT of questions your first few years out and you want them to be accessible) and get good surgical training