It's a valid point that all holograms are not created equal. Instead of "holographic rights," the issue should be one of sentient rights in general, with any sentient being -- whether organic, silicone-based, cybernetic, psionic energy matrix, or whatever -- entitled to the same rights regardless of origin. Although then you do get into the tricky question of how to prove sentience and whether such tests are even ethical (do only AIs have to prove their sentience or should everyone have to?).
After all, strictly speaking, it's a bit inaccurate to refer to the Doctor or Moriarty as "a hologram." Rather, they are AIs that reside inside starship computer mainframes (or inside a mobile emitter or other computer unit) and that use holographic bodies as their interfaces with the physical world. So defining it in terms of the hologram rather than the animating AI is kind of missing the point.