It really depends on your specific conditions.  I need to protect chestnuts in my area.  We have lots of native persimmons.  I haven't had issues with deer bothering persimmon seedlings.  I know others have had issues with deer and persimmons and do require protection.  Of the two, I'll worry more about chestnuts in general.  I tried the "Overwhelm them with numbers" approach and it did not work for me.  I had to go back and add protection.