Like "Space Seed" and "The 37s," "The Neutral Zone" features humans awakened from cryonic sleep being completely outmatched by the greater story around them. In this instance, it's the return of the Romulans and the first tangible evidence of the Borg.
It is a little odd that Star Trek kept doing the cryonic sleep trope, but there you are. I guess the batch in this episode are interesting enough, how they try to reconcile their memories with what they find in the future, but it's a first season episode of Next Generation, and as such it's always at the back of your mind that the series probably would have done this better and more memorably later.
The real story is the Romulans. Slightly less so than the Klingons, they were a featured element of the original series, and not just because they were basically the evil cousins of the Vulcans. Unlike the Klingons, however, Romulans were never a significant part of the first six films (or seven or eight or nine, but they totally dominate the tenth and eleventh!). Their appearance in "The Neutral Zone" is the first of many subsequent appearances in the franchise after this point. They would become a signature species of Next Generation, actually.
Unfortunately, this appearance isn't much more notable than being that first appearance. Most of the story is dominated by those cryonic folk. The Romulans don't have much more of a role than the suggestion of the Borg, who have been skirting Federation space along the way toward the conquest of assimilation memorably featured in "The Best of Both Worlds." It's basically, as one of the Romulans actually says, that they're back. It's a calling card.
But these twin calling cards are still enough to overshadow the main story. In fact, the title doesn't even refer to the main story, and that's pretty rare, but it's also one of the first times modern Star Trek doesn't attempt to use the same naming scheme as the original series, so there's that as well.
Just like that, however, the first season is finally over. Ending it on this kind of note is a sign of encouragement. While most of it is like the rest of the season, there's also the conscious effort to do something greater and more lasting, which like Data's brother Lore sticks in the later developments of the series, and while much of the season tried to establish a separate identity for this generation, returning to the Romulans and especially how the episode does it is a very good idea indeed.
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Memory Alpha summary.