Without a doubt, I would say Majora's Mask. There were a variety of aspects that make it 'darker'. This is not to say that Twilight Princess is not dark - it most certainly was, but I think the way the issues contributing to the darkness, were greater and presented in such a way in Majora's Mask, that made it much darker.
Majora's Mask dealt more with psychological and internal issues - especially with Link - than Twilight Princess. Again, Twilight Princess touched on this sort of thing too, but it was more prevalent in Majora's Mask.
For example, in the beginning of the game, Link is literally tossed into another world that he knows nothing about, with people he does not know, and is in the height of an impending apocalypse. Link's search for his lost friend is abruptly ended and he is forced to save a world he is unfamiliar with.
Further, he only has three days to accomplish said task. This puts an incredible amount of pressure on Link, and stresses him mentally, and physically.
Also, there are all the little things, so to speak. Throughout his quest to save Termina, he encounters a variety of characters, each one relating to another. All of the lives of the characters are intertwined, therefore his actions in one of their lives ultimately affects others.
Another major psychological issue is the fact that each time he resets the Three-Day cycle, his interactions with the people (save for things in the Bomber's Notebook, Temples, etc.) are erased, and reset. Thus, he is the only one who remembers what had just happened. No doubt, this added a sense of loneliness.
Looking more closely at the other characters, they each have their own issues - even outside of the coming apocalypse.
Take Kafei and Anju for example. There's a major issue here, that Kafei can't see Anju, even though he has to soon because of their upcoming wedding, because he had his mask stolen, and more so because he has been turned into a child.
The issue complicates when Anju and her family eventually leave town to go to the ranch to hopefully evade the effects of the devastating impact that will occur soon.
This also leads into another point, that makes it 'darker'. The people of Clock Town (or at least Anju and her family) believe that if they move far enough from the impact site, they will be safe - obviously a desperate and sad situation.
Twilight Princess was dark in the sense that the Twilight Realm was expanding throughout Hyrule, having adverse affects on the Light World, and consequently its people. Hylians were transformed into shadow beasts, and so on and so forth.
Evidently, this is 'dark', and depressing.
In both games, there is a situation that present immediate problems - both apocalyptic. However, I don't feel Twilight Princess is as dark for a number of reasons.
One being that, in the Twilight Realm, it isn't quite as 'apocalyptic' as in Majora's Mask. In Twilight Princess, the people become Twilight beings, or Shadow beasts, and therefore the race isn't necessarily exterminated, as with Majora's Mask, where the whole world is destroyed by the moon.
Likewise, I didn't feel the same sort of psychological affect as I detailed about Majora's Mask. Sure, it was sad and emotional at parts, but it did not have the severe urgency that Majora's Mask did, whilst still managing to retain a sense of 'everyday life'.