Dogs are trainable, because we have bred them to be trainable. I've done a lot of teaching in my time, and my experience with people is that the most trainable are often not the most intelligent . . . In fact, the very brightest are often VERY difficult to train!
Most felines are not social animals and do not have to evolve cooperative behaviors to live in groups. They don't look to leaders and they don't have hierarchies. A cat who is motivated by his own impulses can demonstrate some amazingly intelligent behavior -- They learn to open and manipulate things. We had a cat in the neighborhood where I grew up who learned to ring doorbells. When the door was opened, he would march through the house to the back door and demand to be let out. That way, he didn't have to climb fences. That's pretty high level abstract thinking.
Dogs, on the other hand, live in packs and have leaders, and their nervous systems are all set up for cooperating with others and dealing with hierarchies. They're much easier for us to understand, because we are social animals, too.
I have and enjoy both, but I frankly prefer cats. They don't smell as bad, their personal hygiene is better, their waste is easier to deal with (unless you have a sprayer in your house!), and most of all, they don't BARK.