Personally for me, DS9 was easily the best of the TNG era series (I haven't watched many episodes of TOS & ENT so won't include them in this decision).
The reason why a lot of people prefer VOY & TNG over DS9 is that the story plots often are resolved within the 45 minute episode. We get that closure and return to status quo at the conclusion. Hence single episodes tend to be more enjoyable, and suitable for re-runs. To a certain extent you could randomise the order of episodes in a season and not really notice and each story line and plot is resolved before moving onto the next.
The main characters don't really show that much deep development as the series progresses, and recurring characters are few and far between and often are pretty hollow. The actions that characters made did not really carry any repercussions in future episodes. The major story lines were placed into 2 part 'feature length' episodes. Think about the Borg and Wolf 359 and the Klingon Civil War in TNG and a Year of Hell in VOY. Although Voyager did have more of an underlying story progression, the nature of the show, returning home and travelling in one direction, meant that stories had to be left behind, hence long term plots were not an option.
DS9 however is much more like a soap opera in its structure, in that along with the primary story line that is concluded within the 45 minutes, there are often several story lines that are revisited in later seasons, especially those regarding recurring characters. The multi episode arcs built momentum over the series which made the series a lot more captivating. The final chapter is a 9 episode arc building up to the final episode. Looking outside the main cast, characters like Michael Eddington, Quark, Garrak, Rom, Dukat, Weyoun & Kai Winn appeared in multiple episodes and were all crucial to the shows development.
Another benefit of DS9 was due to its ethnic diversity (ie not everyone being starship officers) it allowed for the boundaries to be pushed and for the types of stories to be expanded. The TOS series written by Gene Roddenberry pushed boundaries by assembling a cast with ethnic diversity all equal as officers, be it the white Kirk, african-american Uhura, Russian Pavel Chekov or Asian Sulu. Boundaries were pushed again such as homosexuality (Quarks gay kiss and Jadzia's brief love with another woman), racism (Ben Sisko as Benny Russell), Black Ops with Section 31, revolution/terrorism (the rise of the new Cardassian movement), religion (Pah Wraiths & Prophets), war refugees (Skrreeans), womens & workers rights (Ferengi Episodes) and the morality of war (In the Pale Moonlight). For me this made the series a lot more interesting and enjoyable.