reading a book by Paul Belasic he said that one way to look at classical verses modern dressage was the pathway to getting to having the horse engaged, collected and on the bit.
The older methods, most suited to horse such as andalusians and lipizzaners, starts the young horse early in a double bridle and teaches the horse to recognized and respect the limits set by the bit/hands early on. Then, as the horse is worked more, it learns to engage the hind quarter more and more until it is not just connected to the bit, but connected through the back from hind to front and carries the rider in the correct manner , which helps develop the spine best for carryint the weight of a man.
The modern school , originating more from Germany, is more suited to the larger warmblood breeds for whom collection is less natural, and extension is more natural. The approach here was more of teaching the horse to engage the hind end and drive forward while the front reaches down and forwward, reaching for the bit, which is less limiiting in the beginning. Develop the forward drive from the hind end, THEN develop the front end boundaries to achieve collection.
Same result from different approaches.