Apologies for not answering your question directly, but I will take the opportunity to voice my opinion on this topic, then move on. In my opinion, the answer is "neither".
For this reason: Too many players in each Hall of Fame.
MLB currently has 351 people in it; the
NFL, 382. (Not all of them are players.)
These numbers dilute the exclusivity of the Halls of Fame. It's as if it is required to induct one, two, three, several people every year because
it is something to do in order to market the halls and the leagues. It's an annual self-congratulatory party.
So which one does it better (or worse)? I will leave that for subsequent discussion. In my opinion, they are both bloated, overcrowded clubs that are becoming more and more irrelevant.