In what ways are The Great Gatsby by F. Scott Fitzgerald and The Sun Also Rises by Ernest Hemingway similar or dissimilar? Similarities insofar as I could extrapolate are the empty, hedonistic pursuits of meaning through love and parties post-war and the rejection of traditional values and morality. Possibly mirroring between Cohn and Gatsby, though the two are portrayed in vastly different lights? Nick and Jake, as unreliable narrators? The most obvious difference to me is the writing styles. Any substantiation upon those observations, or everything else I've definitely missed, would be greatly appreciated—the more talking points the merrier.

I agree with what you have said so far about the two novels. You seem to be very much on the right track!
I might look at the mirroring of Gatsby and Romero, the bullfighter, rather than Gatsby and Cohn—or perhaps use both Cohn and Romero as mirror images of different aspects of Gatsby. (Cohn is, of course, like Gatsby, the despised "non-Nordic," or outsider.)
Both Gatsby and Romero are figures idealized by their narrators: Romero is the pre–Lost Generation male, functioning with courage, lack of self-doubt, faith, and complete virility in a jaded world, just as Gatsby is Nick's vision of the dreamer who is not afraid to think and act with audacious boldness in a corrupt, cynical world—even if his dream is doomed from the start. Gatsby renews Nick's faith in mankind. Both Gatsby and Romero also have sexual affairs with the main female character in their respective novels.
You might also want to look at sexuality in both novels. Jake and Nick may share similarities in terms of being sexually "marginalized" in their time and place. Jake, of course, has been made impotent by a war wound. Some scholars have seen Nick as a gay man—leaning especially into the chapter at Myrtle's apartment when Nick meets Mr. McKee (mc-"key" to understanding Nick?). Nick rides the elevator with him (" 'Keep your hands off the lever,' snapped the elevator boy"—scholars have made much of that, with lever meaning phallus in this interpretation) and wakes up in his hotel room. Both Nick and Jake are lonely (Nick wanders the streets of New York looking into windows after work sometimes) and sidelined in a heterosexual world.
You might also look at the androgyny both Brett and Jordan (down to their names) exhibit, which would have been more daring in the 1920s than today. Brett, is of course, clearly heterosexual, but she does adopt an androgynous appearance, and Jordan may be a lesbian (critics point to when Nick ruminates on her as a liar who is out to protect the requirements of her hard, lean body):

I suppose she had begun dealing in subterfuges when she was very young in order to keep that cool, insolent smile turned to the world and yet satisfy the demands of her hard jaunty body.

I might also be tempted to compare the first Gatsby party that Nick attends to the liminal scene where Jake and a friend go fishing together in nature and share a lot of wine: the types of lyricism are different (the writing styles, as you note, are very different!), but they arguably share a lyrical quality.
You asked for ideas or talking points to be thrown out there, so I hope this helps!