Complex sentence: Some breeds have been selectively bred for hundreds or thousands of years for the quality of learning quickly; in other breeds, that quality has been downplayed in favor of other characteristics, such as the ability to track or hunt game or to fight other animals.
Split into simpler sentences: Some breeds have been selectively bred for hundreds or thousands of years for the quality of learning quickly. That quality has been downplayed for other breeds in favor of other characteristics like the ability to track or hunt game, or to fight other animals.