So really, stats don't really do anything it seems

Got lucky and the store finally let me get some stubbers, absolutely LOVE them but, the stability stat does NOTHING for the weapon, first gun I got had little stability, made it work, braced helps, then the store offers another one with double the stability of previous. Figured, ‘HEY, might not NEED to brace!’ went to the psykanium and saw literally no difference between the two weapons. Non braced on either weapon made the recoil go everywhere as my camera goes wild.

Is it a case of stats not working in the psykanium or just being window dressing period if it ISN’T the damage stat?