This is possibly the most archetypal James Horner score, it is elegaic, understated and ends with a long track that brings all that has come before to a conclusion. It also shows up Horner's weaknesses, much of the material is assigned from other sources (Glory and Legends of the Fall for example). Unlike those two scores, there is nothing unique about Courage Under Fire. Glory had the militaristc stylings mixed with a chorus and Legends of the Fall had the ethnic instrumentation to give the orchestra a little more colour. Courage Under Fire is just the orchestra playing through the typical Horner music.
The Hymn pretty much sets the tone for the rest of the score with slow octave leaps in the bass accompanying a gentle and reasonably emotional hynmal tune. The best track is possibly the second track which is a long action cue that builds quite nicely and is the only track to introduce something else to the orchestral pallete. Opening with helicopters starting up, the pulsing of the rotar blades helps to set the pace of the music well. When the action actually starts it's rather typical Horner crashing about that is elevated quite a lot by a whining electric guitar in the background that reminded me quite distinctly of a John Barry Bond score, although I'm not sure which one! As has been pointed out often, this action music found its way into Titanic, although without the guitars and helicopters and I'd say in this context it worked better. Monfriez's Suicide is quite a disturbing cue that uses some of the action music from Al Bathra and uses some of those clanking anvil sounds that Horner likes so much. It seems a fraction overraught with the onset of the clanging, but being James Horner, I suspect that is works effectively in the film. The Final track brings everything to a satisfying, if unmemorable conclusion.
I would say this is really a score only for hard core Horner junkies as there isn't a great deal to the score that can't be heard with more interesting results elsewhere. The action music (if you're that desparate) appears in a very similar fashion in Titanic and the Hymn can be found on compilations. For a more interesting take on a noble cause during war, I suggest Williams' Saving Private Ryan instead which has the same understated elegance of Courage Under Fire but is much more moving and satisfying.