Interesting question. The FED fund rate is the rate charged between bank to bank lending whereas the mortgage rate is an agreement between bank and citizen. This would lead me to believe that banks give each other better rates than individual citizens.
The FED fund also determines their lending rate every 45 days or so, so % moves more actively than the housing mortgage rate.
Because banks usually have much more collateral they are likely privy to lower rates than indivdual consumers, this would be my best guess, but I must admit it is a guess. Investopedia has good articles for anything to do with money, I'll link one on how the FED rate works. Hope this helps
https://www.investopedia.com/terms/f/federalfundsrate.asp