I can only speak for myself of course, but I find writing for each medium a distinct process with concerns of its own. Here are a few of my thoughts on the subject.
The single most profound difference in the composing process (leaving aside the differences in producing the music in the studio as opposed to preparing it for live performance) is that in film underscoring, for the most part, many critical musical parameters are rigidly predetermined by the visual and dramatic aspects of the particular scene you are writing for. The picture (and the director) tell you when the music stops and starts, to the fraction of a second, as well as its overall shape. This is often very specific—the music must start out very subtly but then 10.5 seconds in it must immediately shift to something with a lot of forward motion, but not too frantic, and be sure the music acknowledges the exact moment when you see the character through the door etc., etc. In concert writing one must also determine how long a piece or section is and where formal changes occur, but that would be left to the composer.
Certain textural considerations are somewhat predetermined as well. You have to be quite careful about being too busy; it is rare that there is much counterpoint, and melody must also be used with care. Often the dialog of the scene is the melody and underscore is accompaniment, or at the least the composer must take into account the placement of the dialog and “leave holes” for it by weaving the melody, harmony, and rhythm around it.
I also find that every small musical emphasis—be it a rhythmic accent, a harmonic change, or melodic leap—accrues a large meaning when played against the picture. One often has to work within a very constricted range of gestures because any time the music draws attention to itself it also draws attention to and highlights what is happening on screen at that moment. This of course is used to great advantage but also must be monitored extremely closely. Rarely can a gesture be made for purely musical reasons, the constant challenge is to find something musical that works dramatically.
A difference so obvious it seems scarcely necessary to state it is that most underscore cues are very short; few are even four minutes long, very few over six. Much concert music is of course longer.
Having said all that, in a given measure of music I’m not sure there is anything that one could write as concert music that couldn’t be written as film music or vice versa. Context is all.