Unlike Data, whose consciousness seems to be a function of both his unique hardware and his software, the EMH is completely generic. It can be distributed purely as software and only requires a sufficiently powerful computer to run it. In "The Swarm" s3x04 a baseline EMH is used to replace the holomatrix of the ships EMH. We see a copy of the EMH from a backup module (probably created to forestall another breakdown as seen in "the Swarm") in "Living Witness" s4e23.
Where Data was able to gain personhood on his uniqueness the Doctor does not have that attribute. Sure his experience and his growth are unique to him, but if you copied them onto another uninitialized EMH you would have an identical copy of the Doctor, having access to identical experiences. That "perfect cloning" directly separates him from most biological species as, without special intervention (transporter accident or mimetic simbiot), duplicating the original entity is not possible.
Also, unlike Data, since the Doctor's personality is purely implemented in software it is possible to "decompile" him and examine the "logic" behind his behavior. We see Dr. Zimmerman doing some of this in "Life Line" s6e24 as well as Seven of Nine extracting portions of the Doctor's personality (his aesthetics) to make him small enough for transmission. This means that his "creativity" and "individuality" is potentially deterministic. Data and biological being may be deterministic, but their processes are obfuscated behind hardware, whereas the Doctor's is plain to inspect. B'Elanna takes advantage of this fact in "Lineage" s7e12 where she is able to alter the Doctors decisions before he makes them by altering aspects of his program.
