Do i like or dislike secret bonus and strength of it depends a lot on bonuses themselves and character management. I voted for minor bonuses and would like to add that these bonuses should be more "roleplaying" ones. And by saying "bonus" i hope you mean not just "secret" and "surprise" but also "no influence on math"
Something that makes person more individual but does not affect SPECIAL game play at all. Something i would call not "perk" but "quirk".
For example some appearance changing like scar in some place or some minor jewelry like ring, wristband or necklace (and hundreds of other trifles character may obtain and like or be unable to rid off).
Another sort of quirks may be minor character behavior while idling or smt, but doesnt affecting game play, only visuals. Examples would be head (or some other place) scratching, constant haircut fixing by shaking/smoothing head... While walking may be stone kicking, while idling silent knocking... Even some minor bad behavior like spitting or nail biting
I hope you got idea what i`m talking about and i would love to get a character with ring in beard
Make n jewelry and m places for it and it would be n*m different characters even in same clothes.