I have been fortunate enough to have a wife who has her Masters Certification in Dog Training. Our household consists of a Border Collie, a Golden Retriever, a German Shepherd, and a black Standard Poodle/Golden Retriever designer mutt.
I say there is a distinct difference between canine "intelligence" and trainability. Our Border collie is the smartest of our dogs but also the most stubborn and independant......she watches and learns - how to manipulate the door latches to get into the bedroom, how to lift the latch to open the gate outside, how to put her paw on the Down button to lower the window in the back seat of the car....she understands probably about 100 different words... but she will not listen to simple obedience commands!
The Shep is almost as smart, but she has a great desire to please and protect. By far the easiest train and she's eager to please.
The Golden is the most trainable (wants to please) but not quite as smart as the other two.
The designer mutt (Poodle/GR mix) is the most well rounded. this dog looks like a 150 lb bear when his coat grows out but he is trained for scent detection/trailing, search and rescue, agility, retrieving and personal protection. When he is not working he is a big clown.
They all are my collective early warning system. the teens around us talk about the "house with all the crazy dogs!". Good 'nuf fer me.