I wrote a couple things recommending that people watch Trek in release order, which means alternating TNG series 6/7 with DS9 series 1/2.
That was a mistaaaaaake. Take each show on its own.
It's difficult to watch these shows together. They're extremely far apart in almost every way, but they have the same setting and sound design, so it's impossible to separate them. The showrunners don't want you to separate them either, and they'll write stories and characters that hop between the two to keep them as firmly linked as possible.
TNG runs to the end of Chain of Command and takes a break for the first four DS9 stories, and then they alternate. Chain of Command is a great setup for DS9, and I like the idea that Picard's recovering offscreen for a few weeks, and who knows what he'll be like when he's back. DS9's initial run is very rough around the edges but it's clear and confident about wanting complicated stories and character conflict. 'Babel' has it all: civilians are in danger, Odo and Quark are fighting, Kira's holding people hostage.
...And then we get TNG's 'Ship in a Bottle'. Picard's fine – a few weeks was all he needed. Some holodeck character's kicking off. I think we're meant to care about his sentience, but since it's taken four years for them to pick up this thread again I'm finding it difficult. They stick the guy in a lil holodeck prison and all is hunky dory. This episode falls short in a lot of ways, but I end up judging it unfairly because over on DS9 there's epidemics going on, all while Picard's so bored he's haggling with the holodeck. That said, the production values are obvious: this is a production crew confident in their craft, nailing the performances and sets and makeup and lighting and so on. TNG is at this point a well-oiled machine, leaps ahead of its first two god-awful years.
...Then there's DS9's 'Captive Pursuit'! After 'Ship in a Bottle', it looks almost clunky – very unsure of itself at least. But it picks the fuck up in its closing moments when O'Brien goes business mode and breaks a guy out of jail. And Sisko lets him do it! Then Sisko does the formality of dressing him down before the two of them share a stifled grin about a job well done. I just can't imagine what this story would look like in TNG, but it wouldn't look like this.
...Then there's TNG's 'Aquiel'. It's fine, I guess.
Going into a DS9 episode after a TNG episode makes DS9's roughness much harder to ignore. Going into a TNG episode after a DS9 episode makes me feel like TNG is stuck, written into a corner, unable to progress. What do you do with a crew of geniuses who all like each other? Jumping between silly and serious plots feels fine when it's the same show, but when one crew's in crisis and the other's playing games it's harder to buy in to either.
Still gonna dovetail DS9 and VOY though. That'll hurt.
Mup from the future
I should've explicitly noted that dovetailing the two shows was, for the intended audience at broadcast time, the "expected" way to watch these shows. It's maybe an obvious point (streaming services didn't exist at the time) but it has a less obvious consequence: there's something of a unique medium in the idea of two separate TV shows carefully riffing off each other to produce a better product (maybe) and do some free inter-show advertising (definitely). Both characters and settings make the jump between TNG and DS9 during this period, which really does work to make the two series feel like they belong in the same universe, and once or twice the medium is exploited for some genuinely brilliant storytelling.
The best example of this is the Maquis storyline. For dovetailing viewers, they get to watch the terrible episode with the Native Americans and the Wesley-pausing-time whatsit that introduces a new conflict, and then they watch that story develop in all its complex beauty over on DS9, and then it's all wonderfully established in time for a TNG character story with Ro Laren. For my money, Ro's episode wouldn't have worked had half the runtime been wasted establishing some new aliens with some new ideas. And then the Voyager pilot can start with its conflict already established and broadcast. Wonderfully efficient stuff.
At the time (assuming what I've read is accurate) crossovers just didn't excite people as much – advertisers didn't go to great lengths to hype them up, and writers weren't required to do anything particularly special with their guest stars. The market of crossovers would eventually be milked though, and more recently this "medium" has become the butt of jokes about shitty new media. "Cameos", "crossovers", and "setups" are things you shove into existing films and shows to get people excited about the "next" thing, and we all call this out as the creatively devoid free advertising that it is. Some of these setups never actually get made into their own things, so your existing film or show is muddied by references to nothing that add nothing whilst still making you wince – great. The interplay between TNG and DS9 feels like a very early-stages example of this, before advertisers had decided this medium needed to be mined to the point of oblivion.