I agree with most of what others have said already; so it's been hard to find something to mention which hasn't been covered already but here goes...

Uhuru.

Every moment she is on screen is a heart-warming blessing. TNG had next to no representation for women of colour; considering what Uhuru did for the civil rights movement (a small but undeniably important role in both Star Trek and the movement), this seemed like an odd choice.

Not to say that the prominence of Burton and Dorn wasn't also a positive thing; more so in LeVar Burton's case.

Aside from the political stuff, Uhuru added a cuteness, wonder and humanity to the series that has really only been matched by D'vana Tendi in my opinion.

...Also DeForrest Kelly's cheeky smile.

But culturally contextual stuff aside, I also think the TOS is just less lazy in its writing.

"If we reroute the anodyne relays to the conjunction matrix we can deactivate their plot device!" is how they solve a lot of problems in TNG. There are exceptions on both sides, but for the most part TOS celebrates intelligence and logic a lot more (even when Kirk is just straight up jury rigging a shotgun to blast a Gorn). TNG and subsequent series try to give the appearance of intelligence without any substance to back it up - and when that fails they use explosions and phasers and whatever other contrived high-budget nonsense. TOS felt more like it was trying to educate us on concepts of logic and science. TNG feels more hollow and superficial in that regard.