Hi Dushin, Here as I promised:
To ride is more than simply “breaking the horse”. Good riding is constant comunication with the horse.
There are three classical “aids” to comunicate:
“Aids” with the reins, “aids” with weight / balance and “aids” with the legs.
“Lower-aids” are the aids with the leg And the “upper aids” normally the aids with the thorso and hips. Some people talks about “lower-and upper ‘leg-aids’”, too.
Very important for riding is the hip. you can communicate with it very finely. If it is tense, or is too skewed, then the whole body can not go with the movement. The center of gravity of the body is also about in this area, so it is important for balance, too.
Many “riding masters” (especially the newer ones) say, that-you will “block” your hip and makes the legs stiff if stretching out your long leg and leaning backwards. This is partly true, but there is another way if one pays attention to the position of the hip.
This could be meant when Dom Duarte says, “a la brida” would block your lower aids.
But the more likely explanation is:
The leg is also extremely important for the communication with the horse. For example, you can steer the horse very fine sideways to the left when lightly pressing with the right-leg to the right side of the horse. Ideally at the right moment when the horse just raises his right hind foot. Also the position of the riders leg is important … more to the front, more to the back … and, last but not least, you have your spurs!
If Dom Duarte says that the rider with an outstretched leg “a la brida” has problems with the lower-aids, then it probably means that the riders must move the leg back to use the “lower-aids”.
An other form of “a la brida” is yust really standing moreorless vertical in the stirrups, but with the leg in the right position for the “lower aids” but can not use them fast enough, because you have all your weight at the legs and stirrups!
But you can compensate all that “lower aids” if you e.g. use stronger the rotation of the hip and ride with the thighs, or the “weight / balance-aids”.
Riding “a la brida” was in mid-northern Europe until the beginning of the 20th century (in an attenuated form) in use.
The long leg is more balanced than the short leg, if you can not only ride for the “art of riding”.
In “a la gineta” one has the leg always in the right position to give the “lower-aids” fast and correct. The leg and the stirrups are exactly under your bodies center of gravity. You have your legs “free” to move them. And you can easily stand up a little bit in a fast and timed way, to “sit lightly” the boincing at trotting.
(In medieval times trotting what not very popular)
So I would say, “a la gineta” is the better choice for riding in the modern way. As a sport for example.
If you want to ride comfortably, then you can make the stirrup longer, and if you need stability, then you can also press into the stirrup. and make a longer leg like “a la brida”.
P.S. For some old riding-masters, riding with a long leg was like those guys in modern days who rides a bicycle witht their hands in their pockets…
“Look everybody! I am so good, I even don’t need my hands” 
