The method of attaching the reins (fig.1), is much more versatile and the reins (having a buckle at each end) can be attached at various heights on the surcingle. The double reins (sometimes also referred to as running reins, but not to be confused with draw reins!) allow for more movement of the head and lead to a steadier contact in the rein from the higher level of play in the rein.
The triangular method (fig.2) of attaching the Vienna reins between the front legs can lead to horses becoming more on the forehand and the horse breaking at the third vertebra. It allows the horse to move his head up a little but the predominant action is in a downwards manner. As there is little room for any play in the reins when used like this, the horse may try to find relief from the niggle felt at every stride by going behind the vertical.
As with side reins, I am neither advocating nor decrying the use of Lauffer reins (aka Vienna or Sliding reins), I am merely presenting them as a training option if you feel horse horse might benefit from them.
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Classical Dressage Notebook