I think they are both great.
I've seen every episode of TNG 1000 times probably, so it definitely feels more stale to me.
Both shows have their strengths and weaknesses I think.
DS9 built on the foundation TNG laid. TNG is the more iconic show. Most people know who Picard, Worf and Data are. Most people will never know who Sisko etc. are.
TNG has an advantage in that you can sit somebody down who never watches Star Trek and they can get into most episodes without having to know a ton of backstory.
DS9 is a show for more hardcore Trek fans. There is more subtlely, more exploration of the Trek universe (strangely, since it is mostly set on a stationary space station).
The DS9 characters grow on a level that the TNG characters never really did. Sure I feel like I know Data, Picard and Worf pretty well. But Troi or Crusher? They are like blank slates in many ways, especially Crusher. I still have no real idea what motivates Crusher or Troi other than broad based likes and dislikes (one likes chocolate..one likes to dance..one is a Doctor..) I don't even know why Troi joined Starfleet.
But with DS9 even the side characters get a lot of exploration. Characters like Garak, Martok, Dukat and Weyoun have more personality than some of the main TNG characters ever did. That is TNG's main weakness and why I think TNG is more friendly to new viewers, but DS9 has more rewards for hardcore fans who watch the shows over and over looking for new things.
But I'm not always in a mood for deep characters and story arcs. Sometimes I just want to sit down and enjoy a good TNG or TOS episode without worrying how it fits into the greater scheme of things.