Now that I've seen the entire run of "Deep Space 9" from start to finish, I have to say that it is far and away the best of the Star Trek franchise.
Part of it's the characters. They were much more fully developed and better nuanced than in Classic Trek or TNG, with dark sides, aspirations, and a wider range of motivations than ever had been shown on Trek before. There were little things, like Sisko's love of baseball; to Odo's uncertain motivation first as someone who didn't know his origins and then as someone who rejected all that his people had done; the moral ambiguity of Quark, who in some episodes seemed decidedly corrupt and amoral and yet who consistently came out on the right side; and there were some really intriguing interactions among the characters, between Garak and Bashir, the repressed attraction between Dax and Sisko, the elaborate dance between Odo and Quark as constable and perpetual criminal suspect, and so on. (And the sheer range of characters! I lost track of how many supporting characters there were, from the station itself, to Bajor, to Cardassia, and the other Ferengi...)
But mostly it was the storytelling. There were some false starts, with the issues surrounding Bajor's assimilation into the Federation, but once the writers got going and started to figure out what the Dominion was and how it worked, the show just kept getting better. Seeing the Klingons as nasties again was a treat, and seeing humanity portrayed honestly on Star Trek for a change -- like in the episode where Garak blows up a Romulan vessel to support Sisko's lie that the Dominion plans to attack the Romulan Empire, and Sisko realizes he's OK with that -- was unforgettable. (And of course there was the episode that suggests the entire Star Trek franchise could be the product of the imagination of a black 1950s science fiction writer...)
I don't think I can say enough good about DS9. It was, all things considered, the high point of Trek. The franchise jumped the shark when they launched Voyager, and it never recovered. Maybe if they really do hire JMS to do a new series, but that's about the only way I can see.