I would say season 2 is a step up, overall. It definitely made space feel dangerous, mysterious, and unsafe. I'd argue it's the one season in the franchise that makes space feel as dangerous as it should feel.
I don't know Maurice Hurley as a person, but his tone and style when crafting season 2 really stabilized TNG and makes him an unsung hero. Danger, mystery, unsafe - it was true exploration and definitely starts to set TNG apart from TOS far more strongly and consistently. The season deserved the same quality of restoration season 1 got.
Plus, we get Dr. Pulaski, who actually had more growth as a character in one season that most of the others did in multiple seasons. (Particularly how she views Data from the start to later in the season.)
Seconded. The Pulaski/Data arc is subtle and strong, had more character growth, is not a McCoy clone (the EMH is closer to that at times)... just a stronger character for any number of reasons, not just the Data double act.
Season 2 definitely had really bad ones, don't get me wrong. "Up The Long Ladder" and "Shades Of Gray" spring to mind. But some of those can be attributed to the chaos in the writing staff that was going on at the time, not to mention the Writers' Guild strike that occured, which is ultimately why we got 178 episodes instead of 182.
^^this
"Up the Long Ladder" has some interesting ideas, but some of it's pure cringe and coasting on an unsavory stereotype.
"Shades of Gray" without the clip show half is actually steeped with atmosphere and a great initial setup, which looks well-made. A shame they had to do a clip show format because of the industrial action.
Season 2 had some great ones, like "Where Silence Has Lease", "A Matter Of Honor", "The Measure Of A Man", "Contagion", "Q Who", "The Emissary", and "Peak Performance".
Silence is one that's steeped in atmosphere and an overall unusual presence.
Matter of Honor is easily first rate and keeps the Klingons shrouded in mystique.
Measure, for me, has gone downhill a bit as nobody would create a sentient being with an on/off switch. But it's still a strong episode.
Contagion is another classic. Computer viruses were not new, but new enough that many in the audience might not see the resolution coming. Even so, everything's tightly written. The Romulans are great. The warp core breach may have been introduced but it was given the level of gravitas needed...
Q Who - the title referring to Q disappearing as if he didn't exist in some allusion from Q's point of view, it's a bona fide classic that introduces the Borg and with supreme menace. It adds to Guinan without demystifying her in the process. Definitely is what the franchise needed.
Emissary - another strong one. Sadly, it's because of this episode that Alexander is made, but not even the 10/10 stories are perfect and this one is a 9/10.
Peak Performance is a fantastic self-contained war story.
Then you have the danger and mystery of space with episodes like (again) "Where Silence Has Lease", "Unnatural Selection", "The Royale", "Time Squared", and (again) "Q Who".
Season 3 gets a lot of the credit for being the turning point for TNG, and while I do agree with that overall, a lot of pieces that help make it the turning point can be seen in season 2.
Unnatural - I'll stand up for this one too. It takes the premise from the old TOS episode about rabid aging thanks to magical radiation ("The Deadly Years"? Its not one of Trek's best...) - but does it with some credibility and not as a whiz-bang gimmick. This episode does bring in the transporter panacea, but in this one it doesn't feel as much of a gimmick either, is held off toward the end, and there's enough threat and urgency to try to save the Doctor - especially when they have to figure out how to reconstruct her as she's never used the thing! This, unlike 'The Naked Now', is how to take an old episode and innovate on it proper.
I might include The Dauphin as well - it's a decent coming of age story handled with maturity by the writers, has a "villain" who is multilayered (the dauphin's
protector and not just a villain with a typical sad origin story) and sold well enough, and the science bit at the start with the machinery that ostensibly rips iron out of blood is a subtle but worthy reminder that space is a dangerous place, even in an advanced shape ship due to its complexity. quite an underrated moment in an underrated episode.
I think of season 1 as the rough draft, season 2 as the one that gets the rest of the kinks out, and season 3 as the polishing finish.
^^this
2 has a couple rubbish episodes but the whole season being lumped into the same category as season 1 is undeserved. (Heck, season 1 isn't all trash and is often pawned as being that in another misconception.)