I didn't grow up watching Star Trek so to say, I started watching Voyager at the end of its run and in re-runs late at night, and didn't delve deep into the Trek universe until the last film came out so I'm sort of a new fan, but with two, maybe three exceptions I've seen every episode of TOS, TNG, DS9, VOY and ENT, and without a doubt, DS9 is the best.
That being said, and I think this has already been touched on but DS9 would not have been what it is without its predecessors. What makes DS9 so special is the way the show is set up to explore the Trek universe, and the writers weren't afraid to explore the dark aspects. They took the building blocks of the Federation we got to know and turned it on its head. Without the other series you don't fully understand the world that is being explored. I also feel that out of all the series, it's the one most relevant to the issues we faced/face in the 20th/21st centuries, and for the most part they approached them well.
Each of the series has their faults and we all know there are at least a dozen of terrible episodes (Masks anyone?) but as a whole the Star Trek television series are done better than the average show that airs on television right now. So I voted that "TNG is ok and I have no strong feelings", although I am re-watching the series on Netflix right now and am quite enjoying myself.
The nail in the coffin for me is that Gul Dukat has to be the best villain to have ever graced television screens.
I think you really hit on something when you spoke about the relevant issues. I agree with you. DS9 feels like a show that could be made today. It was a show ahead of its time in many respects, and I have to wonder if that was one of the reasons for its declining ratings. I've long felt that DS9 was the true inheritor to TOS due to its approaching to draping late 20th century issues in 24th century trappings.