The fight scenes
They're classic "Star Trek" because . . . they often involve close-quarters wrasslin' between two unarmed pugilists. Violence in "Star Trek" typically resembles a Victorian boxing match more than a shootout between 23rd-century gunslingers.
They're "Star Wars" because . . . there may not be lightsabers involved, but these mano-a-mano showdowns often are staged at exceedingly high elevations, not unlike the epic Vader vs. Skywalker battles that took place on precarious footing at Cloud City ("The Empire Strikes Back") and on the second Death Star ("Return of the Jedi").
It's classic "Star Trek" because . . . Kirk has a well-established fondness for alien babes. Both Abrams films includes scenes of Kirk in bed with non-humans, including, in the first film, Uhura's green-skinned roommate Gaila (Rachel Nichols). That's an obvious nod to the Orion mental patient Marta (Yvonne Craig), who makes out with Kirk in the 1969 episode "Whom Gods Destroy."
It's "Star Wars" because . . . there's a classic Luke/Han/Leia-esque love triangle in Abrams' first "Trek" film and, to a lesser extent, "Into Darkness." Presumably (hopefully?) the romantic rivalry involving Kirk, Spock and Uhura won't be resolved when two of them realize they're actually siblings.
The scenes involving spaceships
They're classic "Star Trek" because . . . The way Abrams' camera reveals the Enterprise's famous call letters (NCC-1701) in the film's opening scene is almost a striptease. The fetishistic focus on the ship's iconic silhouette is also classic.
They're "Star Wars" because . . . the Enterprise and its ilk hit warp speed in a way that visually resembles the space navigation of the Millennium Falcon and other Rebel Alliance spacecrafts. There's a scene in the new film that's impossible to watch without flashing back to Luke Skywalker's X-wing starfighter flight through the Death Star's Meridian Trench.