It was a big dogpile, but you kind of asked for it.
What you also might have asked what objective differences between the series make one or other better in people's opinions? For some, it's the originality of TOS. For others, the ethics of TNG. The adventure of Voyager intrigues some. Finally, some prefer the narrative structures of Enterprise. (I'll leave Discovery off the lists until opinions settle.)
DS9 was my favorite Star Trek from the moment it was broadcast, and I have often considered it my favorite series ever since. The two things that immediately struck me that were, shall we say, objectively different than the other series were the attention to family and to the psychology of the hero. Over time the series tried to peal back layers of abstraction (as best much as science fiction can) when dealing with the human condition, and thus in my opinion, helped to make the vision of the previous series more relateable. Indeed, I think that many benchmarks for making Discovery more contemporary were set by DS9--personal failure, decisions over ethics and Realpolitik, earning trust, telling a continuous story, etc. And more concretely, Section 31 has become a pervasive counterpoint to the more idealistic ethics at the heart of some series.
