The rivalry between Star Trek and Star Wars is as old as the stories themselves. Fans of either are some of the most dedicated and loyal fans of any form of entertainment. On the surface, the rivalry seems to be Science Fiction fans arguing over ‘Which one is better Sci-Fi?’, and to many it might be as simple as that. The lines of fandom have been drawn similar to sports teams’ rivalry. If you look closer, you’ll see just how far they are from each other in deeper meanings.
This article will explain differences based on the basic STORY components of Star Trek/Star Trek: The Next Generation and the original Star Wars Trilogy in comparison to each other. All else (characters, worlds, etc.) will not be addressed specifically unless necessary. I personally am a fan of both franchises and will try my best to remain objective and not fuel the rivalry further.
When comparing the original Star Wars Trilogy with Star Trek and Star Trek: The Next Generation (TNG), three major themes stood out to me as important to each as well as directly opposing each other.
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Science VS Belief

In both franchises, Science and Belief play pivotal roles. Star Trek takes the approach of Science over Belief while Star Wars promotes Belief over Science. The series focus’ on the crew of a spaceship named the U.S.S Enterprise that is part of The Federation. The crew uses science to solve any challenge they come across in their journey through space. Usually the conflicts of an alien civilization that they help resolve are based solely on a conflict of belief. In the episode “Let That Be Your Last Battlefield” the crew interact with aliens that are in a race war that originated from a Belief that one race was superior to another. The crew attempts to help them understand that all life is equal, but the beliefs of the aliens are unwavering. That belief led them to the destruction of their entire species despite the crew’s efforts to help them. This theme, that peace can only come from acceptance of differences, carries throughout the series. Different alien civilizations have different conflicts that usually started from a difference in belief. Sometimes that conflict ends in the alien species’ self-destruction.

Star Wars has the complete opposite message. ‘The Force’ is a powerful plot device in Star Wars. Those that Believe (have Faith) in ‘The Force’ are able to interact with it and, with training, gain supernatural abilities and the title of Jedi Knight. The protagonists are Luke Skywalker, Lei Organa/Skywalker, and Han Solo who eventually join the Rebel Alliance. The antagonists of Star Wars are the Republic, who rely heavily on technology. Spaceships, weapons, and sheer numbers are in favor of the Republic, leaving the Rebels outmaneuvered, outgunned, and outnumbered. At the climax of all three movies, the deciding factor is the power of Luke’s faith. His Belief in ‘The Force’ is what allows him to destroy the Death Star. A lack of Belief leads him to defeat against Darth Vader in The Empire Strikes Back. When his Belief is restored, he is able to help Darth Vader return to the Light Side of The Force. Belief is the absolute power in Star Wars.
Star Trek promotes the idea that Belief eventually leads to conflict, while Star Wars promotes the idea that Belief is the only way to achieve peace.
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Free Will VS Predestination
Free Will is a focus of Star Trek. The crew has no other mission than to explore the uncharted reaches of space. Each episode features the captain stating the premise of the series:

Space—the final frontier. These are the voyages of the starship Enterprise. Its five-year mission—to explore strange new worlds—to seek out new life and new civilizations—to boldly go where no man has gone before. (Star Trek)
Through their journey they remain adaptable to any situation. Destiny does not play a factor in their experiences, their actions do. All crew members have unique personalities but all are able to adapt to most situations. The Federation views all life as equal and worth protecting, even in situations of hostility. The people are the ones attempting to bring order and peace to the universe through their actions.
Predestination is a major factor in Star Wars. The Force has a strong connection with the Skywalker family. That connection allows them to become powerful Jedi compared to anyone else. This also plays into the message that Destiny is predetermined and a person’s actions only determine which path Destiny will follow. In Empire, Yoda (Luke’s Jedi Master) tells Luke:

Stopped they must be. On this all depends. Only a fully trained Jedi Knight with the Force as his ally will conquer Vader and his Emperor. If you end your training now, if you choose the quick and easy path as Vader did, you will become an agent of evil. (Yoda, The Empire Strikes Back)
Despite Yoda’s warning Luke leaves, showing his lack of Belief (Faith) in the Force. When he faces Vader, he succeeds in saving his friends but fails in defeating Vader. His decision to leave his training put him on the path to failure against Vader but saving his friends had a chance to succeed or fail, it relied on him.
Star Trek promotes the idea that there is no Destiny, while Star Wars promotes the idea that Destiny is predetermined and people can only choose which path to take by their own actions.
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Chaos VS Balance

In the Star Trek universe, there is no over arching structure to the universe. Each society is attempting to bring order to their environment in the way that they see fit. The Federation seeks to promote a peaceful existence in the universe whereas the rival governments and organizations (Romulan Empire, Borg, etc.) have their own ideas on how to bring order to the universe. Opposing ideas on how to bring about order to the universe lead to conflict.

Star Wars promotes the idea that there is a balance between the Dark and Light side of the Force. The original trilogy starts with the Dark Side in power and through the films the Light Side gains strength and overthrows the Evil Emperor which brings balance back to the Force. This plays into the Belief and Destiny aspects of the story in that everything revolves around the Force.
Star Trek promotes the idea that there is no structure to the universe and that life must find a way to survive, while Star Wars promotes the idea that the universe will always find balance between Light and Dark regardless of any decisions made.
Closing
The differences in the two stories are opposing but there is no clear winner or loser and that is what makes them both great! Fans are able to choose which connects with them individually. Maybe that’s another factor in the rivalry. I personally enjoy both and I don’t hold these differences against either of them. As the years go on I do believe that the rivalry is not as severe and more people are able to enjoy both of them for the amazing stories that they are!