true sentience will stall in favor of the cheap knock-off
If that was true, there would be only cheap knock-off science, and in fact first rate science exists.
Which has more value (from an economic view): True sentient AI or an excellent mimic of human behavior
Current AI systems do not correctly mimic human behaviour. Rather, it averages out human behaviour, with all the limitations which this implies.
"Sentient" means having sense perception, consciousness, sensation, feeling and subjective experience. I doubt any AI could ever be proved to possess consciousness since we cannot even prove that other humans have it, but sentience seems irrelevant to economic value. So, the crucial distinction is not between human-mimicking AI and sentient AI, it is between really intelligent AIs and AIs which are not really intelligent.
Today, we only have the latter. Presumably, current AIs can have or gain at some point a very high economic value. Good for them. Yet, this is nothing compared to the potential economic value of a really intelligent AI. Think of an AI which has the same sort of intelligence as humans have, but without the limitations of the human biology.
Because of their biology, all humans spend most of their time on Earth either sleeping, eating, defecating, reproducing, watching news, talking about the weather, exercising their body etc.
No human can think all day long, let alone 24/24, 7/7, 12/12.
The human brain also has a limited capacity, which we are very unlikely to be able to increase significantly any time soon, which is why collaboration between humans is crucial.
However, humans cannot communicate with each other very effectively. To convey our ideas to other people, we have to use either verbal communication, which is terribly slow, or the Internet, which itself requires us to painstakingly key in our messages, exactly what I am doing right now. This is also terribly slow.
Humans cannot also think very fast because our brain is a biological brain. The human brain is a very remarkable product of natural selection, but just the same it is really slow.
We also cannot learn very fast. Typically, any truly new idea requires days, often weeks, sometimes months or years of learning. In fact, new ideas often requires several generations of humans, sometimes, often, many new generations of humans, as history demonstrates.
Sometimes, new ideas requires entirely new technological means, like the telescope, particle colliders etc.
Humans cannot also hold in mind many ideas at the same time, which despite our good logic is a terrible limitation and explain a good chunk of the terrible stupidities that we all commit throughout our lives.
Think also of humanity itself: How many humans can even afford to spend time to think beyond matters of personal immediate survival. Civilisation found a work-around by institutionalising education and providing academics with the ressources to survive without having to hunt or grow food themselves. Yet, most academics only produce limited economic value. The ones that produce high values are so few that, out of billions of humans who have ever lived, they are like Einstein known by their personal names.
Humans also have many cognitive biases, which are most of the time evolutionary solutions to the many problems endangering our survival, but often are not conducive to higher intelligence. Humans spend more time fighting and killing each other than they spend in thinking ideas having an an economic value.
Truly intelligent AIs would have the potential to be literally awesome. Just beyond anything humans would ever be able to do without it.
For good or bad, though.
oOo
Edit: What is the distinction between intelligence that is personal property (dogs, cats) and intelligence with human rights?
This is a completely different question. I would have thought that there is at least for now a large number of obvious distinctions between dogs or cats on the one hand, and any AI computer on the other, but if we could make an AI computer exactly like a dog or a cat, and if we recognised it the same rights as dogs and cats, then by definition we would all accept that there is no apparent difference. I don't think this could be even possible in practice, though.
However, also by definition, an AI computer which is exactly like a dog or a cat still is not a dog or a cat, unless you are using a private language nobody else understands. So, as long as we somehow believe that the computer is a computer and therefore neither a cat nor a dog, it will seem very reasonable to rational people to keep treating it as a computer and not as a cat or dog.
So the difference as always would be in what we happen to believe about the computer.