General Kaliero
F = ma, beeyotches.
I own both games (OoT in multiple versions) and Zelda is my favorite game series of all time. I was introduced to it through OoT. I still play OoT to this day, simply because it's such an amazing, fun game. However, I also absolutely love Twilight Princess, as it's another brilliant game. So let's just go through this category by category.
Gameplay: As far as combat goes, TP wins this. It starts out with all the moves OoT had, but then adds more onto them. All of the Hidden Skills to learn make battle more interesting and ultimately, more fun. Also, horseback battles are excellent, fun and fast-paced. Items are also an important part of the experience. OoT's items were just about perfect, with something to use in any situation. The Magic system was also good, though the only really useful magic was Din's Fire and the magic arrows. TP drops most of those items (and the ones that come back are slightly altered) and does away with the magic, while adding a few items we've never seen before. Some of those items may not have been extremely useful (poor neglected Spinner...) but they are all interesting and at least fun to use. I think TP comes away with the better items. As for minigames, that is my one gripe with TP. Its minigames are few and far between. OoT easily beats it, with minigames all over the place.
Story: An interesting decision here. TP has the technically better storytelling, with a superb epic feel to it and deep personal connections. Yet OoT still feels like it was the perfect Zelda story, with Zelda petulantly commanding Link to do what causes exactly what she wanted to prevent. It all comes together at the end, and essentially creates a perfectly closed, well-told story. It's a hard decision, but I have to throw the better story to OoT. Character-wise, though, I think TP has it. The only developed characters in OoT were Link, the Sages, and Ganondorf. In TP, nearly everyone you talk to (right down to the sweet girl that runs the fishing hole) has some background, and they are all in some way interesting. Even Link, stoic, silent Link, manages to display a personality on emotions alone. And of course, I have to mention Midna here, who is the best, deepest, most well-developed and real character in the entire series, ever. Again, the characters in TP are an absolute joy.
Again, both are excellent games that deserve every honor given to them, but overall I have to say TP edges out over OoT as the better game.