1. No Wesley. I can't stress how much this makes a difference. Nothing personal against Wil Wheaton, but the conception and execution of the bubblegum perfect future boy strains credulity (by halfway through the first season, he was in regular rotation flying the Enterprise; by the time he left the ship, he was basically a bridge officer) and guarantees three or four unbearable episodes a season until the wide-eyed little bastard finally gets into Starfleet Academy. Then he comes back for numerous obligatory late-season cameos, each a lowlight eclipsing the last until the borderline offensive one with the Native Americans and Wesley running off at the end to becoming a being of pure energy, or whatever. At least in doing so he proved unavailable for the films. Cirroc Lofton's Jake Sisko by contrast has a wonderfully formed (from the first), touching, and realistic relationship with his father. And unlike Wesley, he wasn't first in his class in everything. He was a regular kid who disapointed his dad (pursuing a career as a writer rather than Starfleet) and got in trouble for doing stupid things (a lot). There's a lot of camaraderie in your "Star Trek" shows but not a whole lot of realistic, strongly developed parent-child relationships. I mean, but for the one where Troi got impregnated by Tinkerbell.
2. Alone among "Trek" shows (and most other TV) it regularly and often critically examines religion. The original producers, although they exerted little direct control after about the third season, set the show on the right foot in the pilot by dealing with the fact upfront that the Bajoran people, around whose planet the space station orbits, are a majority religious society. Their religion is heavy on ritual and light (in modern practice) on restrictions but their church's leadership is intensely political and decidely secular in its behavior. The first season ended rather quietly with a religious drama (involving a suicide assassin) that was low on action, but led into a three-part second-season curtain-raiser that involved the Bajoran church's direct collaboration in a military rebellion. Kai Winn, the faithless, ambitious prelate who becomes the leader of the religion in early-season intrigue, is a villain from the beginning and becomes a monster by the end. But the show doesn't lack for positive religious figures either. The saintlike Kai Opaka is too wonderful to work well as a storytelling device for all that long, and is martyred right away. Many others follow, ethical to varying degrees. At the show's climax, the Bajoran "prophets" become an essential part of both the development of Sisko's character and the resolution of the other major storyline of the later seasons, the all-encompassing Dominion War.
3. The crew isn't the best and the brightest. The first Enterprise was assumed to be the best ship in the whole Federation -- clearly, since all the other ships kept getting blown up by Klingons or Tholians and Kirk et al always got out in time for the last commercial. The second ship/show was built on that model, all the way down the line (see also 1. No Wesley). The skeleton crew assembled to look after the abandoned Cardassian space station in "DS9" would not be there if they could have the same jobs on super awesome starships as big as Zapp Brannigan's. O'Brien takes the job because he's a career noncommissioned officer and it's his opportunity to be a chief engineer instead of a transporter operator. Kira's there against her will, because the provisional Bajoran government finds her opinions annoying and her status as a hero of the resistance politically threatening. Dax is a fairly new ranking officer in the guise of Jadzia, as a joined Trill she's socially compelled to avoid generations of former lovers hanging out in the hotter spots of the galaxy (and it's also not every Federation commander who's totally comfortable working with 300-year-old aquatic insects, even ones with hot babe shells). Bashir is a seeming exception, he tells us he had his choice of assignments, but later on we find he had a compelling reason for wanting stay well under the radar as far as job placements were concerned. In short there's far more opportunity for conflict with a bunch of marginal Starfleet officers with murky pasts (or past lives) than there is among the annoying rah-rah "Next Gen" crowd. Kira and Sisko start having shouting matches immediately, and Odo and Quark's enduring mutual (non-Starfleet-aligned) hatred is one of the enduring hatreds of all television science fiction. It's good when regulars argue! They do it on "Battlestar Galactica" all the time I bet.