There are several great replies here thus far. However, I believe something else needs to be considered - the nature of the consciousness created.
Data has a positronic brain. This implies something fundamentally different than the "conventional" quadritronic processing done in Starfleet computers. The fact that the "quad" and its various metric system designations (e.g. kiloquad) seems to amorphously float between a measure of memory storage and processing power doesn't help explain what the difference is one bit, but then, neither does the designation "positronic brain," which is what's used to describe Data's brain.
I think, however, that the best way to describe Data would be more along the lines of Data being more hardware-bound in many ways. That is to say, that Data's core brain is physically more similar to an organic brain than a computer. While it is not a pile of goo with neurons and synapses, it is probably akin to morphware, which is basically hardware that reconfigures itself like software.
The Doctor and other holographic systems rely on much larger and more powerful, conventional computer systems. This may well mean that these holograms have a rather different form of consciousness and sentience, in that they are essentially "simulated persons." Philosophically this may mean that they are "less" than people, or don't have true consciousness at all, but the audience generally assumes that at least the EMH is sentient. Nevertheless, if this is indeed the case, chances are there are differences that are at least oriented towards their subjective qualia, leaving Data's "experience" to be much more like that of a conventional organic being, yet with the advantages of a computer.
However, we should not be quite so hasty in judging just what the Doctor is. The Doctor's computer systems were unique on Voyager. In one early episode it was stated that it would be impractical for him to be transferred off the ship and out of the sickbay systems (Voyager episode Life Support). This implies some sort of specialized hardware, since otherwise he could be brought, if need be, in a few suitcases of isolinear chips. Let us ignore for the moment that he'd almost certainly have ended up vivisected (or decompiled, or whatever the equivalent is for holograms) by the Romulans for his technology in that particular case.
Another thing that suggests possibly specialized hardware for the Doctor is the fact that the mobile emitter CAN apparently separate the Doctor from Voyager entirely. Furthermore, it does so in a rather illogical manner from a computer science perspective, specifically that the Doctor seems to cease to exist in the Voyager computer, as opposed to a copy being created. Whether this can be a comment on the technology backing him, or an example of the writers ignoring or being ignorant of computer mechanics, is difficult to determine, and I'm pretty sure it was never addressed. Looking to the mobile emitter is of little use. I'll bet the Federation can copy it and repair it, but it will be a considerable time yet before they understand it. Nevertheless, this does show that it's possible that the Doctor uses more than conventional computing power to attain sentience and consciousness. He may well use some sort of (until the mobile emitter, unmovable) Data-like brain for at least part of his program. However, that doesn't mean that there's a giant copy of Data's brain behind one of the walls in sick bay; this could just mean that he's got a processor in there somewhere that takes care of a certain portion of his cognition with most of the actual processing being in conventional computer systems.
Nevertheless, since it seems (to me, at least) that the evidence weighs in that sentient holograms are still running MOSTLY on conventional technology, this leaves Data rather unique. Even if the holographic AI allows Starfleet to produce new, intelligent beings, the process by which the sentience occurs is still different from the way it does in a person, which has scientific value on its own, and may have functional value that is not obvious. It is also noteworthy that this would have some objective consequences as well as subjective consequences. While we are not equipped, as an audience, to determine these, as we know little about the technology, a major one comes in the form of actual programming. It is possible that Data's "programming" is considerably different than what would normally be considered programming. Furthermore, he seems to be resistant to external programming attempts, considering his confidence in the face of Borg coercion. The EMH, on the other hand, is modified as a program several different time during the series, and is also subject to "orders" from the holodeck program he's in, such as falling under hypnosis because the program says so (Voyager episode Spirit Folk). Whether or not the crystalization of a structure producing consciousness is a criteria for considering it to be actual or merely emulated consciousness is a decision for the Federation courts, I suppose.
So in short, one major thing that renders Data unique is HOW he is made into a sentient and conscious being, and that it is probably in a manner much more similar to organic brains than what would be produced by a hologram.
Now, THAT mouthful out of the way, I have to agree with other posted assessments in many ways. Remember that Data's been around and operating for several decades and has probably been poked in just about every part of him in one way or another. It's not impossible that they've figured out a lot of how he works. In fact, Data himself volunteered for some of Dr. Maddox's experiments once he was sure it wasn't going to kill him in the process (TNG episode Data's Day). It's not unthinkable that Maddox indeed perfected the experimental technique, ran it on Data harmlessly, and managed to come up with a way to replicate positronic brains. Further, we have at least two instances where positronic cognitive hardware were introduced in the series. Lal, first and foremost, produced a complete, if unstable, positronic brain, that in fact lived for several days (TNG Episode Lal). However, another thing that suggests that positronics are considerably more advanced is what happened with Vedek Bareil (DS9 Episode Life Support). He had half his brain replaced with positronic equipment, and although it made him something of a technozombie, he was nevertheless still a conscious being. And Bashir implied that he could do it for the rest of his brain, though refused since Bareil really would be a technozombie if he did it. Although it could be retconned back that the only reason Bashir could do this was because he was a super genius, it seems like it's a bit of a stretch, especially considering it would be almost impossible to cover up that he managed to cook up this plan all on his own on the fly even though the best engineers in the Federation had been slowly piecing together the puzzle of just how it worked for decades, let alone deliver a fully functional medical application.
Furthermore, as in the extracanonical material, Data was revived in B4, it is likely that reverse engineering of that extent was revolutionary in the understanding of the positronic brain. With this in mind it is possible that Data's resurrection may have simultaneously answered many of the questions that remained. Plus, if I recall correctly, Data basically "promised" B4 that he'd make him a new brain as B4 was essentially reversibly replaced with Data's mind. This gives Data a VERY direct reason to find out a way to make a new brain - both to give his brother a new positronic brain to exist in, as well as try to help him overcome any limitations of the hardware that Data can likely bypass due to superior programming, but B4 may be restricted by.
So in short for THAT text blob, most of the references to Data's uniqueness were in TNG, and furthermore we saw at least two examples of technology's progress making that uniqueness a far shakier prospect.