In keeping with its focus on military conflict, The Undiscovered Country has a more epic feel than its immediate predecessors did.
The film is darker than usual. And no, we don't just mean that in terms of tone—this thing is literally dark. It's a deliberate choice on director Nicholas Meyer's part: Enterprise is usually brightly lit, in keeping with its sleek futuristic aesthetic, but here, the darker Enterprise makes us feel the tenseness of the situation much more viscerally.
Similarly, Meyer decided to make the hallways of Enterprise smaller than usual to give them a claustrophobic feel. Both of these choices heighten the intensity of the film, specifically emphasizing the fear and tension associated with war.
Another consistent production choice is the use of tight close-ups on faces. This choice ties in with the film's use of lighting: characters' faces are often framed with dramatic shadows. Again, it's a way of heightening the film's dramatic intensity and establishing a darker tone than its predecessor, The Final Frontier, had.
The Final Frontier featured rocket boots and a group singalong of "Row, Row, Row Your Boat," for Spock's sake. You've got to put in twice the work to makes things feel dramatic after that.