This is a very difficult question.
I have fond memories of both franchises, which grew over me throughout my childhood and younghood. I had briefly played FF IV, and my first "real" FF experience started with VII, which I absolutely loved, although not with some frustrations along the way. Regarding Zelda, I never knew anything about it until my father installed the N64 emulator on PC (yeah, humble beginnings, didn't have money for a console back then :P) and I decided to download the Ocarina of Time rom, which sounded like an interesting game. After being annoyed by the initial wtf where do I go now (I was a kid back then, the rom was in English and my knowledge was next to zero), and the game opening up after beating the first dungeon, I was in awe.
Fast-forwarding some years, I had the pleasure of playing FF III, IV, VI (never played 5) and VIII. I loved every single one of those, my favourite being VIII because at the time (and it still is) it struck me as the most magical game I've played, in a metaphorical sense. Regarding Zelda, I also had the chance of playing Majora's Mask, A Link to the Past, the original one and Wind Waker. Outside the original one (which I didn't really like much), those games were also an immense joy to play. A Link to the Past and Wind Waker are masterpieces in both 2D and 3D departments. I have to admit, in shame, that I didn't beat WW until a few years ago, though; mainly because I didn't own a gamecube, and I had to play at my uncle's house.
So, which one I prefer? I guess I can't really decide. For some reason these both games tend to get lots of complain, but I loved every single second of Final Fantasy XIII and Twilight Princess. I guess the only Zelda I haven't been able to properly enjoy is Skyward Sword, and that one is at the very end of the chain. However, playing Awakening DX on my 3DS was truly a joy, so all is forgiven.
I've yet to play some missing Zelda and FF games (like The Adventure of Link, The Oracle games, FFX and FFIX). If you have to force me to answer, then I'm going to say Final Fantasy, based on the fact that the VI-VIII era doesn't seem to get archaic in any way, whereas I can't seem to go back and replay Ocarina of Time. That and coupled with the fact that FF VIII is still one of my favourite games ever conceived, yeah. I say Final Fantasy.
