A large parrot has around the same number of neurons as a beagle dog.
Combined with weight savings, this may allow their brains to work faster, which is useful for a flight computer.
Birds have other features which are superior to mammals. For example, their flow-through lungs allow for more efficient gas exchange.
However, having to fly means weight reduction has been a big driver of evolutionary compromises. A bird that can fly cannot carry large fat reserves around. They are not resilient when sick and often die quickly after the onset of visible symptoms.