All you have to do is look up the definitions given in the 'Webster's Universal Dictionary' for these three words - dressage, competition and classical.
Dressage - the training of a horse in deportment and obedience.
Competition - act of competing; rivalry; a contest in skill and knowledge; a match.
Classical - influenced by, of or relating to ancient Roman
and Greek art, literature and culture; traditional; serious; refined.
In the United States, when most people speak of the Andalusian, they are referring to both the Pure Spanish Horse of Spain and the Lusitano of Portugal. In Spain, the term Andalusian won't be heard unless speaking of horses from the region called Andalucia, in southern Spain. Still, in the United States, you will frequently see the name 'Andalusian' be connected to the Pure Spanish horses, since it is more correct to call the Portuguese horses 'Lusitanos' .
These horses have been bred for centuries, long before the Europeans began to breed horses for sport. And that is where you'll find a major difference between the Andalusians and today's modern sporthorse, the latter being what competition dressage was designed around. The Iberian horses were bred for things quite different from sports. They needed heart, courage, strength and a high degree of collection for fighting the bulls and excelling in the very fundamentals of classical horsemanship that are studied today.
In the (now popular) historical books on training, you can see these horses being trained in a variety of 'high school movements' and 'airs above the ground'. You could say these horses took to this kind of training readily, or rather the training was based around these horses' abilities. Both are true. This training was very serious, suitable for royalty and often considered a true art form. This form of classical training has been maintained throughout history in a small number of places where horsemanship is shown as an art. And if you haven't noticed, the horses used for this training have always had a high degree of Spanish (or Portuguese) blood in their veins.
The modern sporthorses of today needed a competition for them, to show their abilities in the dressage arena. Notice I say "dressage" arena, not "classical dressage" arena. The need to show extension became important, coinciding with that need in the other sport forms. The competition was divided into tests, which were shown at different levels of training. The levels show the horse progressing from the very basics to the extreme in extension and collection. This is all well and good for these horses and they do it just fine at all levels. You may notice the Spanish types do best when they arrive at the upper levels, when higher collection is required.
The Andalusian can go through these tests equally as well as any 'warmblood' type, yet the picture will and should obviously be a bit different. Some people will prefer the look of low, extended movements of which the warmbloods excel and others will prefer the higher, more collected movements of which the Iberian breeds excel.
The idea of "lightness" seems to have a new popularity today. Many people believe it's easiest to achieve the ultimate in lightness with the Andalusian rather than the warmblood. This may be because of the "finished picture" you get in the end. The knowledgeable trainer can train either horse to be just as 'light' in his hands and aids, yet the Andalusian will typically make it look more eloquent and effortless, since they are built so balanced and naturally able to collect easily. This is what these horses were bred for and centuries of breeding is going to prevail.
These horses can compete very well in sport, but they will always be in a class all their own. As far as 'dressage' goes, I feel they are able to show their wonderful abilities best in 'classical dressage' rather than 'competition dressage'. When a horse is so gifted in what we consider an art form, why do we feel a need to change him to fit into sport?
They do just fine in sport already, many showing their superiority in extreme combined driving competitions. Some of the best are Lusitanos. John Whittaker took a famous Lusitano, Novilheiro, to the top in Grand Prix jumping, after the horse excelled in Grand Prix dressage competitions. These horses truly are "well rounded."
If you show your Andalusians in dressage competitions, don't be discouraged by judges' low scores in areas of 'extension' or 'freedom of movement'. These scores are very subjective. Your horses can actually excel when performing the tests accurately, with great transitions. I know, because I have placed first in tests against plenty of warmbloods, simply because the test was done more accurately.
Just an added note - there is now an opportunity for owners of 'baroque' horses such as the Andalusian to compete in dressage competitions designed for them and their natural ability to collect. The first "Trophaeum Mundi" competition was held in Portugal in 1996 and was highly successful. These competitions will be held around the world. You can get more information by calling it's founder, Mr. Jean-Philippe Giacomini at 713-286-1659.