As shipbound series, TOS and TNG showed us glimpses of the Star Trek universe. DS9 took that picture and gave it depth. Rather than just seeing them as aliens of the week, we got in-depth looks at the Ferengi, the Cardassians, even the Klingons. They were not guests, they were part of the fabric of the show.
Look at the characters. TOS was about Kirk, Spock, and McCoy. TNG was about Picard and Data, with some storylines for the other five regulars. Voyager was the Janeway and Seven show, for the most part. Deep Space Nine had more recurring characters than regulars. We had humans, Bajorans, Cardassians, Ferengi, even a shapeshifter, all with their own stories and arcs.
Look at Sacrifice of Angels. In addition to the regulars, there are ten recurring characters. Each one of them has their own fleshed-out backstory. Several of them find the culmination or turning point in their arc here. Many recurring characters see more screen time than the regulars.
TOS showed us Klingons; DS9 shows us what it is like being Klingon. TNG showed us the Federation, the "good guys" of the galaxy; DS9 showed us the Federation under siege, what it would do to remain good. Voyager showed us a crew that became a family; DS9 has a myriad of people, good and bad, who learn to trust each other.
DS9 dealt with politics, religion, and conflict. This does not mean it is not Star Trek. The original Star Trek was "Wagon Train to the Stars." DS9 is what happens after the homestead is established, and what it takes to build a life out on the frontier.