As a kid playing both I'd pick OoT, but now I'd say MM is the better game, ironically both situations being because of the 3 day cycle mostly.
It IS annoying to play with (which is why as a kid I hated it), but as some other people have said what it let them do with the game is incredible, as unlike anything else I've seen the world actually feels alive since every NPC is off doing their own things during those 3 days and it changes between the days, even just little things. For instance, if I remember right, the monkey held by the dekus gets moved out into the center of the room near the end of the 3rd day, stuff like that. That and how things change depending on what you do is really cool (everything to do with the ranch).
That, and as I'm older I appreciate the atmosphere of the game so much more, it's so dark and gloomy if you start looking beneath the surface. Best example I can think of are the sisters at the ranch, where the older one promises the younger one she can try some of their alcoholic (not explicitly stated but damn well implied) product near the end of the 3rd day. On the surface, nice. Thinking about it, the older sister knows the end is coming and she's going to let her younger sister get drunk beforehand to make it easier. I may be completely overthinking it, sure, but having such a strong atmosphere that actually allows stuff like that is awesome.
Not to mention I think gameplay-wise MM is probably the best Zelda. The dungeons are large and maze-like, and stone tower temple is pretty damn awesome with the flipping, and the bosses are easily the best in any Zelda game as they can be beaten in multiple ways and provide an actual threat (both of which are generally lacking in later Zelda games, especially the first bit).
Overall MM comes out on top for me, but only on stuff I appreciate now that I didn't care about as a kid really.