They're much better than standing martingales (I think what you call tie-downs). Standings are used for stuff like gymkana games and horseball (I have a feelign they are mandatory for horseball, actually) for obvious reasons, but I wouldn't use them otherwise. For a start it is completely unsafe to jump in them, which is why they are banned from official jumping competitions.
Yeah...so basically, the reins are run through two rings, which are then attached to the girth, making it harder for the horse to throw its head high when and only WHEN the rider exerts enough force on the reins. This allows the horse the ability to recover itself in a dangerous situation and near fall, as for many things they need to either raise their head up or stretch out to regain balance or to jump - standing martingales do not allow this.