I used to really like both shows, but I ran into problems with some decisions that the VOY writers made and dropped the show about the same time I think Lynx
(from the VOY forum) did.
The straw that broke the camel's back was when Kes was dropped in favor of Seven of Nine--a move that seemed like it was strictly for sex appeal. As odd as the whole Ocampa thing seemed sometimes, Kes seemed like a real woman. Someone you could almost expect to be living in your own universe, not this unrealistic person. Her beauty seemed like the healthy kind. Instead, they ditched her character for this forbidding canon violation of a Borg and dressed the actress in painful, claustrophobic cat suits for the sake of appealing to the teenage boy demographic.
The damn thing of it is, I actually LIKE Jeri Ryan. I thought her work in Boston Public to be far superior and I even remember a plotline or two that took on the objectification of women in a manner that really made you have to THINK about the subject. So this isn't Jeri Ryan hate, by far. It is what the show became because of what the writers chose to do with her that I did not like.
With the introduction of Seven, I also felt that the writers threw every bit of continuity about what happens with liberated Borg, what their natures, reactions, and so on are like, that had been established in "I, Borg" and "Descent." Now, I'm aware a lot of people hate those episodes, but I was a great fan of them, and to me Seven's lack of evolution as an individual flew in the face of all the evidence we saw in those two episodes. (Hell, if anything, Hugh's failing was that he typically erred on the side of too MUCH emotion, not too little, so Seven acting like she had no feelings at all just did not fly.)
And don't even get me started on the rest of what was wrong with the way VOY handled the Borg.
I also have problems with seeing Janeway as a consistent and capable commander--a problem that is not a sexism problem at all: I have the same comment to offer when it comes to Archer and nuKirk (even old Kirk, to a much more limited extent). Sisko...yes, I am willing to call him on his bad decisions, and boy he made a few that still make me fume--but if you had to ask me who I'd want as my commander, he's my obvious choice, head and shoulders above any of the rest.
The lack of serialization, as others have pointed out, was a missed opportunity. When DS9 headed that way and VOY didn't, I really felt like an opportunity was missed. We should've seen, like nuBsG, the cumulative effects of their voyage. That doesn't mean having to be AS grim as nuBsG, by any means, but we should've seen SOMETHING. Instead, they apparently had a shuttlecraft-sized replicator stashed somewhere and endless power to run it, at the same time as they were under "replicator rations" for their food.
The concept began with a LOT of promise. But when the show foundered, and the poor ratings stunt of Seven of Nine was brought in to try and "save" it, it jumped the shark. It's a damn shame, too, because it could've been a lot better than the way it went out in the end.
Now that said, obviously I am a HUGE Niner and I do consider it the greatest Star Trek achievement. I have bones to pick about ENT, TNG, and TOS (in descending order), in addition to VOY, and I simply cannot enjoy those shows the way I do DS9. But I do not idolize DS9 to the point where I think everything is perfect about it.
NOR do I feel the need to go and proclaim some sort of "Niner superiority" all over the rest of the board. I am content to like what I like and let others like what they like. People's reasons tend to be very personal for that sort of thing (as are my reasons for no longer liking TNG). That's on me, not on everyone else. The reason I am saying all of this is because we are in the DS9 forum on our own turf. I would NOT go into anyone else's section of the board and trash what they like--that's not right at all.