Brain size is not generally seen as a reflection of intelligence in dogs or in other species.
That is evident if you compare other species with different brain sizes — for example, elephants and people: People are far more intelligent despite the huge disparity in physical size.
Intelligence has more to do with the development of different areas of the brain over the course of evolution and the devotion of different areas to specific functions. The potential development of the brain is equal among the various breeds.
However, not all animals develop equally regarding genetics and environmental influences. There could be marked differences in intelligence between dogs of nearly identical breeding, even litter mates. And as any Chihuahua owner could tell you, some of the smallest dogs can be some of the craftiest.
Dogs were selectively bred over millennia for different kinds of intelligence and behavior. People who have tested dogs with obstacle courses and other measures of talent have found that some breeds excel in particular areas, such as herding or retrieving.
Some, like the border collie, German shepherd, and poodle, seem to excel in many fields.
