I'm making a cavalier that's going to take the Order of the Saddle. The effect for the Challenge is this:
Whenever an order of the saddle cavalier issues a challenge and is astride her mount, she can charge the target of her challenge—moving and attacking as if with a standard charge—and then move again as if using Ride-By Attack. Her total movement for the round can’t exceed her mounted speed. This maneuver provokes attacks of opportunity, but the cavalier gains a +1 dodge bonus to AC against attacks of opportunity while charging the target of her challenge. This bonus increases by 1 for every 4 levels the cavalier has. If the cavalier already has the Ride-By Attack feat, this dodge bonus increases by 2.
Ride-By Attack allows for double movement speed in a charge. So would the effect from the order override the feat against a challenge target?
Since both mount and rider are charging, it should work with either mount or rider. Whichever one has the feat should roll the check.
Personally, it makes more sense to me for the mount to make the overrun maneuver (realistically, it's the one doing all the work of overrunning), and that's how it worked pre-FAQ, but we're in a brave new world now.