I'm glad I ran into this thread because I just finished my Season 1 run through for the firs time in several years.
In watching the series start to finish for the second time now, I remembered Conspiracy as the season ender, but I was wrong. I got Conspiracy and TNZ confused.
And that's because Conspiracy, even years ago, was more memorable to me than TNZ.
Though Neutral Zone reestablished the Romulans as a threat, the 20th Century subplot felt like an awkward, amateurishly written episode. It was entertaining enough, but I didn't think it came together the way Conspiracy did.
Conspiracy was a much better episode, for me, because it was suspenseful, entertaining and I felt like the good guys were in mortal danger. Something that was lacking in Neutral Zone. Sure, the Romulans were back, but so what? It was all talk. In Conspiracy, the threat is PRESENT.
It's too bad this arc went nowhere. An invasion of Starfleet by an alien force had so much potential.
I didn't like what happened to Remmick. He was a smug S.O.B. and was unlikeable when he was grilling the Enterprise staff, but by the end, he started showing some of his humanity. I would've liked to have seen a little more of Remmick before getting killed off, because I thought his character had potential. He was more interesting than the Admiral IMO.
I also thought the aliens had potential to be developed. They were killed off "Aliens" style, but there seemed to be a hint of greater albeit menacing intelligence there, and it's unfortunate that it was no explored further.
I also thought it was good that Picard cknowledged their holding life precious, but were forced to kill. This was a line of thought that deserved to be explored as well.
Overall, I thought Conspiracy had more to offer. It wasn't executed perfectly since there seemed potential to explore any numbers of threads it presented, but that might've been corrected if they had followed this story arc further.
Neutral Zone was all bark and no bite, and it had a EXTREMELY clumsy subplot.
My vote goes to Conspiracy.