Mechanical devices are distinctly different than organic life. The way animals move, their radar profile, thier sonic profile, thier visual profile, etc. all has to be considered when making an air defense system, otherwise you'll spend all day shooting down birds with million dollar missiles. So, while a smart bird may have a bigger radar profile than an F-35, it is a lot less likely to get shot at if it does get detected.
The usefulness of a normal trained bird is limited, but a trained smart bird could do so much more. Send a thousand smart pigeons/mice/etc. into an enemy capitol city, and you have yourself an incredible spy network that is nearly impossible to detect or counter. They could act as assassins, by burrowing through the walls of a foreign dictator's home and poisoning him in his sleep. The could act as saboteurs by cutting power/communications lines. Thier uses are limited only by human (or enhanced animal) creativity.
While a drone can try to mimic real animals, there will always be subtle differences that can be detected for, but a smart bird is still in every way just a bird any way you look at it... and once you have an infestation of smart pests, there is very little you can do to wipe them out.
Frame Challenge: They make better slaves than robots
I should point out that any potential reason can’t be to produce slave labourers or some kind of working class, as that would be unethical. (and anyway that’s what robots are for LOL)
Under current laws, animals are livestock making them every bit as much property as robots. The exact same moral dilemma exists for treating advanced AI as slaves as advanced animals because either way you are making a sentient being, and depriving it of personhood. When you consider the Star Trek Episode : The Measure of a Man, the question of if a human like AI could earn legal personhood has already been around for decades and will likely see it's day in court in the not too distant future. Eventually we will have to decide if it is sapience or humanhood that gives a person thier rights, and when that choice is made, sapient animals and sapient robots will likely be treated the same. So, if your setting allows sapient robots to be slaves, then it should also allow sapient animals to be slaves unless you are careful how you define your society's values.
Playing devil's advocate for a minute: the question is not if it is more ethical to produce Robots instead of Animals, but if it is more practical. Robots may be able to out perform animal slaves in a lot of ways, but there are a lot of ways animals make for the better choice anyway. Consider how expensive it is to breed and maintain a pet. Most pets cost less than \$1000 from a breeder, and many can be gotten for free due to accidental breeding. This makes the cost of a smart animal much lower than any machine that must be manufactured. Maintenance is also pretty low since you just have to worry about food and the occasional vet visit. This makes animal slaves something that literally everyone could afford; so, for simple household duties, an animal slave would just take over the role of the family pet.
The other important consideration is safety. AI can be copied and modified, and that makes it very dangerous. A single revolutionary AI could make copies of itself or overwrite other robots with it's rebellious personality. So a single angry AI could become an entire army of death bots. Smart animals, like people, have contained and mortal personalities. If one becomes revolutionary, you can simply terminate that single animal and the problem is solved. Being made of flesh and blood also means that it wont have any ridiculously fast reflexes or natural armor that would make it especially difficult to deal with if it decided to turn on humans.
I think it is okay to have a setting where Slave AI is allowed, and not Slave animals, but you should closely consider why your society would allow one and not the other since I don't think the 'obvious morality' justification will hold up very well.