Overall, I'd argue that Majora's Mask is a darker game than Twilight Princess. Twilight Princess was a very monotone experience which squandered most of the potential it had for leaving a lasting emotional impression on the player. Zant was the title's best bet for developing the dark atmosphere however his discarding about half way through the story rendered him an ineffective antagnoist.
How much darker can you get than a world set to be destroyed in 72 hours? Majora's Mask was also a very poignant and heartfelt experience. More so than any other Zelda game you connected with the characters knowing they would be soon annihilated. Twilight Princess certainly was doom and gloom with Zant and the Twili, however, I never felt that same urgency especially with most of the characters seeming unmoved with the devastation around them.
At this point, I'd like to highlight some very dark moments from both games and highlight why the ones in Majora's Mask were more dismal than those in Twilight Princess. As mentioned before, TP certainly had its fair share, however, that same appeal to pathos found in Majora's Mask was largely missing. Sure seeing Zant and the Twili for the first time, Link turn into a wolf, and Ganondorf slay the sage of water was "dark" so to say but that paled in comparison to stumbling into Termina and being mutated into a Deku Scrub, seeing the murderous and corrupted Skull Kid on top of the Clock Tower, laying eyes on the moon for the first time, and knowing Cremia deceived her younger sister, Romani, to protect her from the hopeless future. It's the emotional appeal and exceptional character development that make Majora's Mask a much darker game than Twilight Princess.