You will notice a difference with more or less trail. Frinstance a MTB or Touring bike is generally very stable and easy to ride no handed, a racing frame will be much twitchier feeling and less stable. For example my old mountain bike is much easier to ride no handed and much more forgiving than my Soma Rush, but both are rideable no handed. On the MTB I can eat a sammich, and zip my jacket all while going around a corner no handed. On the Rush if I absentmindedly shift my weight I'm veering out of my lane.