I grew up watching reruns of TNG during it's first run with my older brother, so it will always be special to me. It's one of the few things we still share and and have in common. That being said, I credit DS9 with making me the Star Trek fan I am today.
While I thoroughly enjoyed TNG and respect what they accomplished not only from the standpoint of a sci-fi show running in syndication, but also laying down the ground work which DS9 was built on, TNG was still just a show I watched.
It wasn't until DS9 came along that I started caring about the universe in depth and trying to find things beyond what was merely shown on screen in those weekly episodes. I needed to know the details of the world and DS9 was the framework which provided the desire to begin that deeper investigation.
It's a bit ironic though, because at the time DS9 began, I can remember not being interested in it at all. I can remember some of those early commercials that would air while TNG was running and just wrote it off as something I didn't care about. That went on until TNG finally ended and DS9 was in it's third season. I happened to see an episode by chance. I had been watching something else and left the TV on while I was drawing...the episode was Heart of Stone.
With that one episode, I was hooked. That story between Odo and Kira pulled me all the way in. I saw Defiant and The Search in the weeks that followed and quickly realized that DS9 was not anything like TNG. Even in those season three episodes, they were doing things that were setting the show apart from TNG.
I had to learn more and began a quest to find out everything I could about what I had seen in those few episodes. I think I had missed the TNG episode where Thomas Riker was shown, so I had no idea what was going on there. Who were these shapeshifters and why was this Odo guy some sort of outcast or refugee. Obviously he cared for Kira deeply and that was part of it, but there was also obviously more.
And what was up with this ship, the Defiant, that had little to nothing to do with exploring, and everything to do with kicking ass.
For a while, it was difficult to answer these questions because I didn't have the Internet back then. I watched as much DS9 as I could, and soon discovered that there were in fact Star Trek magazines that I had no idea had existed. That also started my interest in moving beyond weekly TV installments of the other sci-fi shows I was interested in. Sci-fi magazines catered to a variety of sci-fi shows, many of which I was already watching. I read everything I could get my hands on, from cast interviews, episode synposis I hadn't even seen yet, and even the TV Guide which used to do a pretty good job of covering Star Trek.
I can remember that by the time season 4 of DS9 aired, I had a pretty good handle of what was going on. TV guide had run a special with Worf on the cover, since he was making the move from TNG and it covered some of the background I think.
So unlike most of my friends, who might have had jobs, or were obsessed with bands or whatever they happened to be into, I spent the later years of my teens, obsessed with DS9, Star Trek, and sci-fi as a whole. This provided a sort of new appreciation for TNG and TOS as well. Because now, they weren't just shows and movies, they were integral parts of this larger world. The things that TNG had done, introducing the Caucasians and the Bajorans (easily my two favorite races in Trek) mattered in DS9. Without the world TNG had forged, DS9 never happens, or at the very least happens in a much different way.
So while I love DS9 (of course I'm not saying it was perfect by any means) and I may at times criticize certain aspects of TNG (such as poorly developed female characters) I have nothing but respect for the TNG and the work done there. TNG is a classic in every sense of the word. Science fiction on TV, would not be what it is today, had TNG not paved the way. We all owe everyone that was a part of TNG a debt of gratitude for the work they did.