James Horner is probably my favorite film composer, but he gets a bit of flack for "borrowing" cues from other composers, and reusing his own themes in multiple projects.
My thought is that he's just a student and lover of music, and whether it's "borrowing" or an "homage," wasn't trying to fool anyone. Nobody would try to claim motifs and cues from composers as famous and as widely heard as Prokofiev or Copland as their own.
Just for fun, here are some samples of Horner using similar styles, or almost exact cues, from other composers. I pulled some of these from various lists, but many of their video links were broken, so I've found working replacements. Some of these YouTube videos allow embedded viewing, but others don't unfortunately.
Star Trek II
First, compare Battle in the Mutara Nebula with this part of Prokofiev's Alexander Nevsky.
Star Trek III
The previous example was at least inspired by Prokofiev, but this section from the destruction of the Enterprise scene is practically identical to Juliet's Funeral from Romeo and Juliet.
And speaking of Juliet's Funeral...
The "Stealing the Enterprise" scene is one of my favorite from all of Star Trek, partially because of the great music. Compare the opening of this scene with "Death of Tybalt." James Horner seems to be pretty fond of Romeo and Juliet!
It shows up again in Willow!
An American Tail
Copland is another of my favorite composers, and apparently Horner was also a fan. Though I'd say this track from An American Tail is a bit more on the "copy" rather than the "homage" side of things...
While Goldsmith scored Alien, Horner did the sequel. There are some similarities between Aliens and Khachaturian here. I've read that Cameron wanted to channel a bit of 2001: A Space Odyssey here, which itself used Khachaturian.
Revisiting Willow you'll notice quite a similarity to Schumann!
Prokofiev has to be Horner's favorite composer. Here he channels parts of Ivan the Terrible.
Battle Beyond the Stars
Now this one is a bit odd. Battle Beyond the Stars was released in 1980, just three years after Star Wars, and one year after Star Trek: The Motion Picture.
In general this score seems to be a rough draft of Star Trek II. You could play large parts of this score and I would probably say it came from Star Trek II if I didn't listen too closely.
This was early in Horner's career, and I can only imagine that he loved this score, but didn't get a chance to do it right with the time or budget he had, so he perfected it for Star Trek II. You'll note lots of cues and other ideas that are heard again and again, but appeared here for the first time.
This opening track has powerful cues that are almost identical to Star Trek II. And is that Goldsmith's Patton?
Now for the very odd part... This movie came out one year after Star Trek: The Motion Picture, for which Goldsmith did another of my top favorite scores. The beautiful "Illia's Theme" is probably my favorite piece he ever created.
And one year later, Horner just uses it in Battle Beyond the Stars:
Oh, and don't forget Krull (1983):
As Stravinsky apparently once said, "A good composer does not imitate, he steals."