They started out with basically a hybrid of Voyage of the Space Beagle and Forbidden Planet, merging the scientific expedition in space with a military space adventure. The two go together like peanut butter and jelly, and gave Trek a distinct feel from other sci fi. It is slightly more highbrow, and more concept-based than action-based, with a dash of sex appeal. Kirk and company are kickass heroes, but they almost always turn the tide by thinking about the situation for a second and coming up with an idea.
Modern Treks have tended to be more sexy than smart, more flashy than contemplative. The science and technology are usually nonsense, and often aren't even internally consistent. They make a big deal about Lt. Data being an advanced android, but he demonstrably isn't. Mudd's Women were far more convincing simulacrums, and the technology in the holodeck can whip up a better AI on the fly. And they usually don't get the process of either science or engineering right, because they skip over the process and jump straight to the solution.
I'm a big fan of the original series, but the science and technology was just as nonsensical and inconsistent as in TNG/DS9/Voyager. I think TOS was definitely more ground-breaking for science fiction at the time, and often did a better job of showing process, but I think the episode writing of all four series was always a mix.
I think TNG had a terrible setup and characters - along with a horrible first season, but it had good actors, and it had some really great episodes particularly into Season Three and Four. The example of Data isn't particularly inconsistent or inaccurate. Data was not intended to pass as human - he deliberately had non-human appearance and affect. For example, it was established early on that the technology existed to give him emotions - he just didn't have it included. He was for sure superior to the android in I, Mudd (not Mudd's Women). Even if he didn't have emotions, he didn't have smoke come out of his ears and break down when confronted with illogic. He would at most be puzzled and question it.
The holodeck could come up with superior AI, but only by using the power of the room-sized ship's computer, as opposed to Data's human-sized brain. In the original series, androids were only built by technologically-superior non-human civilizations (in "I, Mudd" and "What are Little Girls Made of?"). The most advanced computer from the TOS Federation was the Daystrom ship-controlling computer that went off the rails, and was only marginally AI.
I feel similar to Armchair Gamer that where the franchise lost me was after 2000 with Star Trek Enterprise and the reboot movies along with Enterprise (along with Discovery and Picard - though I haven't watched more than a little of the last two).