The second season begins with more powerful events through Mr. Spock, where Kirk discovers that his first officer must return to his home in Vulcan, where it seems to be about getting married or dying. On the other hand, Kirk disobeys his orders to save Spock at those moments, trying to find the uneven Vulcan in his throat. Perhaps it may be different especially when the bride pays the race to a duel, and chooses the captain as her hero at the time.
While it's arguable whether it's better than the first season, the second season of Star Trek: The Original Series contains many of the show's most memorable episodes and introduced characters and lore that helped make Trek what it is today.
In fact, by the end of the season, we're fully convinced that the crew of the Enterprise would rather die than violate the PD, and that means something.
