It's really hard for me to say. I was a huge TNG fan at the time and loved Trek in general. So I was going to give DS9 a huge change anyway. And, after all, I had nothing to lose since TNG was going to be on the air for a few more years anyway. So why not have two Treks instead of just one?
I thought Emissary was a solid start. And although S1 as a whole was pretty rocky, I enjoyed DS9. It couldn't touch TNG at that point but there was no reason for me to stop watching.
Come season 2 I felt the show had grown stronger, and I myself became more attracted to the Bajoran storyline. TNG was still in the lead but DS9 was doing some catching up.
Obviously, at this point VOY was already in development. I was extremely excited about ANOTHER Trek show, and for a while this was what I was looking forward to most. Interestingly, sometime before DS9 S3 and VOY S1 aired, I noticed that I had actually grown more excited about a new season of DS9 rather than the launch of VOY (is that prophetic, or what?).
Anyway, I remember being really impressed by the Defiant. I'd never seen anything like it on Trek. And the huge fleet assembled by the Romulans and Cardassians was also like new territory in addition to the things that already set the show apart.
By S3, I admitted to myself (quietly) that I actually liked DS9 just as much as TNG. Not that I'd have ever stated that in public
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I think the point where DS9 really, REALLY got me was The Visitor. I think no TV show had ever touched me quite as much as that one episode did. I found it absolutely amazing. I also realized that it could have only come from the building of characters that DS9 had done so well over the years.
With S4, DS9 just skyrocketed IMHO and left TNG in a plume of dust. I was totally hooked, and couldn't wait to see what would come next. The show was darker, more complex, more serious, yet also more fun on a certain level. And it was a lot harder to guess what would happen as events with the Dominion, the Klingons, the Cardassians, and the Rolumans unfolded.
The rest is history, so to speak. When I went to rewatch DS9, the one thing that struck me most is how excellent Emissary was. This is IMHO easily and by far the best pilot a Trek show has ever done - period. It's complex, engaging, moving, and it does a terrific job of introducing the show and its characters. Honestly, if I had to rate it on a scale of 1 - 10 for the entire series, I'd give it a 10 without even flinching. And interestingly, as I grow older I find that particular episode only becomes more appealing and relevant.
The only other show to ever truly challenge DS9's position as my favorite show (and I think it's probably succeeded) is nuBSG. But I still hold DS9 in very high esteem. It remains one of my favorite three shows (nuBSG, DS9, B5).
