I seem to hold a minority view here and I'm not sure I have the vocab to explain why.
The philosophy of consciousness has a long history and although there is now a structured field of study, we are no closer to an answer. The question of consciousness is such an elusive one that we don't even know how a general anaesthetic works, or even if it exists universally, in all animals or even people.
When I look at a group of people, I know that they are all like me. They all have opinions, dreams, hopes, dreads, desires and needs, and that behind those eyes there is someone driving. That when I am not there, they still continue to experience their own existance. This is what sets people (and animals probably but thats another argument) apart from electrical/machanical "thinking" machines like my laptop.
I don't like to use the word soul because it has paranormal/religious conotations but stripping those away, and removing any hint of eternal existence after death etc, I still think it best describes the essence of a person. What I have, and what I am, behind my eyes, looking out at the world and considering my next words is my soul. How this soul is created in the brain I do not know, but its not the accumulation of knowledge and experience. I know that my brain is not a computer despite some of the apparent similarities. Likewise, a computer may emulate some brain functions, even replace them, but the conscious experience is a unique function of the brain.
Now, back to the trek world. Data is special because his positronic brain is special. It has gubbins that mimic biological brain function, the electrical fields and technowaffle give Data his sentience because its the same process. Its unlikely in the real world, but its not an original Trek concept and I can accept it as plausible in the context of the show.
Trek computers however have been shown to be rows of circuit borads, chips and the crew utterly indifferent to its non-physical needs. There has never been an episode dealing with the computer's non-physical needs. It never had a nervous breakdown. The Hal 9000 was portrayed as sentient and the crew had casual conversations with it. It also went mad. But we saw the Discovery through the eyes of Hal because the writer/director wanted us the think of Hal as being like us, but artificial. This is not the case with Trek tech, that intent is just not apparent in the writing or direction.
Infact, trek portarays a world as dumbfounded by consciousness as us today. If they had solved the connundrum, there would have been no question of Data's rights as a person. A simple technobabble test would have solved that problem, as with the exocomps. The same test would have been apllied to the computer and its holograms.
The Moriarty stories worked nicely as a 'what if?', but we leave it there and tune in next week and watch a 'what if' we breed super humans with aggressive immune systems, or even, 'what if' theres a writers strike and they do a clip show... My point being that sentient holograms are an interesting idea, but even the Moriarty character wasn't proven to be sentient, they just assumed he was because he acted that way.
Running with the idea throughout Voyager was a bad move because it wasn't consistent with the rest of trek tech and the ethical questions it raised were very limited. If a computer gives rise to sentience, a thinking mind, cheapens everyother character in the trek universe because it essentially trivialises the meaning of life. It makes existence a purely mechanical process and quantity of life was placed above quality of life. Life in trek is cheap because it can be created at whim, but that conflicts with the life is sacred do no harm attitude.
The same issues are posed by the dipiction of the transporter. The original being destroyed infavour of the copy. The original is killed. Under those circumstances, nobody would ever set foot in the transporter room. Its like transferring your job to a new town, but instead of moving, they just hire someone just like you and put a bullet in your head. Your conscious mind is not important, the job is still being done, there is still a 'you' walking about. Trek has confused sentience, intelligence, consciousness, computers and life and the soul in to one meaningless mess. I can't think of any episodes where they have shown disembodied consciousness, but how would that work for machines?
The point I am trying to make is that making the EMH sentient was to raise various ethical questions about what is life etc, it was to make him a colourful believable character whose life could be placed in jeopardy, to be just like us. Thats fair enough, but to me, and this is reinforced by everything I can find to read on the matter, sentience is linked deeply with that ineffable something that most people call the soul. That ineffable something is not to be found residing in a calcalating machine, however complex it is, or however convincing the simulation might be.
The EMH issue would have been better used to explore what it was to have a soul, what it meant to be alive, the whole sum of our parts and wotnot. Instead, we find it just being another civil rights debate. They never checked their holodeck simulations for any other sentient holograms that might have popped in to existence before ending the simulation, would that become murder? Some believe in the afterlife, some believe in reincarnation, while other believe in the impenetrable cold brick wall of death that ends our existence. I envy all of them because I simply do not know. The sanitised athiest future never addressed how the futurefolk will cope with their mortality and its a far more intriguing subject than the Doc's love of classical music or whatever.
Just look up sentience on wiki, and the follow the links and references on the dizzying ride of confusion into exactly how little we know.