TNG was pretty damn popular, even during its first season. It looks bad now when have the later, better seasons to compare it to.
At the time, a lot of kids sorta liked it but thought at lot of it was hokey too. The groundbreaking effects-creation methodologies to provide then-reasonable quality by using newer videotape editing techniques for effects (phasers) creation, combined with actors that somehow managed screen presence (they all pretty much had!) despite the joke that circulated in 1987 that "Data is the most human character in the new show", the aura of Trek was still at a high point with the Kirk movies, and lack of other big-budget sci-fi shows airing 26 episodes a season (Dr Who, the only near-contender, had lost out due to its 1987 season looking and being absolutely stupid, never mind 13 half-hour episodes were transmitted as omnibus 4 stories for most PBS stations.) TL;DR prevailing, the ratings numbers were enough and the show got another run - of which I know I'm thankful for! TNG's evolution is a rare thing, on so many levels.
TNG is very special to me, but DS9 is a better show overall.
DS9 feels the most TOS-like with character conflict, but more expansive in plot scope and potential. And ironic, since the first three years had them largely stuck at a galactic bus terminal and not on a ship - but that didn't prevent the show from putting out a lot of great stuff. The Defiant definitely helped, but early on it wasn't needed - they had enough plot strands to make it more than viable.
For me, no contest, TNG wins by a mile. In fact (get the tar and feathers ready), if you add in the other ST series as well, DS9 is still at the bottom of my list. It is a dreary soap opera in a sci-fi setting, with seasonally redundant plots (Kardashians take over, or nearly take over, DS9; Federation and Klingons team up and defeat Kardashians; next two episodes everyone complains about the mess left by the Kardashians).
I'm liking that post for the misspelling of "Cardassians". DS9 did have soap opera but it also had a heck of a lot stronger action and setup than TNG had.
In a way, they were aiming for "realism" in a continuing serialized arc instead of the standalone episodes where they would reclaim the ship at the end of the episode and in the very next it look like nothing ever happened.
DS9 did have some redundant/recycled plots, including what you'd brought up and others... sometimes they did it better (Starship Down > Disaster ^42) and sometimes they did it worse (Sarek > Dramatis Personae (^42(^42))). But some of the redos of war arcs still had me hooked *blush*. There are only so many plot types but before I get to the best comparisons I'll get to them:
TNG had redundancies and redos all the time: Among other examples, "Measure of a Man" was done several times over and only with diminishing returns, by "The Quality of Life" they weren't merely sleepwriting they were in a coma and using the cut'n'paste functions in word processors...
TOS too and they had THE best! They had umpteen examples of "Kirk vs the Computer where he verbally nags it until it explodes - unless it's the Enterprise computer being affected in which case they sic Spock onto it so it leaves the ship
without being destroyed in an odd twist o' fate". Another oft-used gem: "Kirk on the planet they equate as being Eden despite giant albino unicorn apes or Snake Mountain with beach towel-wearing hawt dingalings or the hippie planet with the deadly vegetation", "Planet of parallel Earth development so we can raid the wardrobes instead of having to make new things but we'll sleepwalk through those too because "100 years ago we left a bunch of copies of the same book for everyone to read and the book was about gangsters so now we're on the planet of the Bonnie and Clydes" or "we're Yangs or Kohms with a perfect copy of the constitution and Flag designs", NaziWorld, the generic nameless 1960 world (that doubled as Bonnie'n'Clydeville) for Miri, Planet of the Flappers (1920s, something they missed out on but consciously so since Kirk would be all over that map), and so on.
All that glorious sardonic nitpicking doesn't mean all these instances are hideously bad by default or 'just because', within a myriad of qualifiers and constraints they relied on what seemed popular at the time, to varying returns. Key themes did remain popular so why not reuse them as much as characters... or both at once, like the Borg (they even used 7's origins, twice.)
A lot of '80s TV also wasn't really that great. So TNG S1's quality issues might've been less noticeable.
Style over substance, some A-Team and Knight Rider were okay (of which some have held up reasonably well) but the 80s often had nothing more than vapid cartoonish action or truly lame soap opera.
