Equilibrium is difficult to classify. Let's begin with its face value: It is apparently a science fiction movie about a future totalitarian society which forces its members to eradicate all emotion by means of a drug for the noble purpose of avoiding war and conflict, which are consequences of emtions, of course.
The movie is quite a complex convolute of allusions and quotations. The main character, who ultimately turns out a Neo-like liberator, is member of an elite troop called Tetra-Grammaton (which incidentally represents the Hebrew four-lettered name of god), but being called Clerics, they very much remind us of the Spanish Inquisition, the Jesuit Order or an even more sinister version of Opus Dei. Since they have to protect the system against the underground resistance (who do not take the drug), they are first rate fighters of course who have developed a gun kata, a kind of sword fight with pistols - smart idea, that! There is also a lot of Nazi symbolism and behavioural patterns, like kids spying on their parents (but ...), and 1984 is being quoted frequently, too (lots of really huge screens with "the Father" preaching). So, plenty of things remind us of the Matrix trilogy, not least the fighting choreography. On the other hand, it is also a nice éducation sentimentale of our hero - touching how he has his emotional Damascus experience by accidentally listening to the opening scores of Beethooven's 9th symphony.
But is it a science fiction? In my book, science fiction is obviously not reality, but it has to be at least credibly imaginable, thinkable, and thus "realistic", given the proper societal and technological development. In Equilibrium, that is not the case (I am not sure about Star Trek either, btw). A society in equilibrio would die of instant "heat death", in my view: Human robots without emotion and thus motivation would just not "work" for any extended period of time, let alone a generation or so. That's the crux of the film: Its foundation is utopian in the classical sense of the word: It is nowhere land, it is unthinkable. But it is fun trying!