To compare the difficulties of the two games, I will use my experience from the first time I played the games, and I will be using the original games of Ocarina of Time, not the Master Quest.
I played Ocarina of Time after I finished Twilight Princess, and I found OoT harder than TP. Mainly, I look at difficulty from the perspective of dungeons and bosses. And in both of these cases, I found Ocarina of Time to be harder than Twilight Princess. I actually got stuck a few times in the Forest Temple, Water Temple, and Spirit Temple in Ocarina of Time, but other than the Lakebed Temple, and maybe in the City in the Sky, I never got stuck all that much in Twilight Princess' dungeons.
In TP, I did not see the bosses progressively get better that much as in Ocarina of Time. Argarok, where he should have been very hard, wasn't very much harder, than say, Morpheel. But Bongo-Bongo and Twinrova, for me, were somewhat more difficult that say, Barinade and Phantom Ganon.
Work to be done in between the dungeons was also harder in Ocarina of Time, in my opinion. I didn't know right away that after finishing the Water Temple that I should go to Kakariko Village. But I never quite had a moment like that in Twilight Princess.
I know both games like the back of my hand. But even when I didn't, OoT was still the the harder of the two. TP was just too easy. I never got stuck once. Even the boss battles were incredibly easy. Even Ganondorf was too easy. OoT was much more difficult.
On top of that, OoT wasn't nearly as linear as TP. In TP, the game made sure you played through it in a certain order, which made it much easier for me to figure out what I had to do next. OoT was different. After you get the Master Sword, you could pretty much go ahead and complete whichever dungeon you wanted first. It wasn't very linear. I even got lost a few times. On top of that, OoT didn't really specify on how to solve certain puzzles within dungeons. TP did, on the other hand.
Overall, TP could hardly give me a decent challenge. In fact, the only thing that presented a problem for me in TP was the Cave of Ordeals. I died a few times there, but not enough for me to consider it a good challenge. I can now easily complete it in one go. The Gerudo Training Grounds in OoT was probably the hardest part, next to Ganon's Castle. I still have a little trouble with both of those, even though I've beaten them both about ten times.
When all is said and done, I'd have to say OoT is more difficult than TP. OoT presented a good challenge for me. TP was dissapointingly easy for me.
On a strictly fresh play with the games either playing them for the first time ever, or playing after having completely forgotten everything in them, Ocarina of Time by far. But I do think a select few puzzles in Twilight Princess were harder. But the game as a whole was far easier. It felt like it was aimed to a wider, more casual audience. And casual players hate difficult games. In the earlier days they were less concerned with that and more concerned with making the best with what they had. That was before the days where you had widespread casual internet games, mobile games on phones, etc. They didn't have that to compete with back then. Now they do. So I guess it was out of necessity. Though personally I think they could have done that by just having a few more casual games rather than sacrificing a major series to the casuals.
Definately OoT. If anybody has ever read any of my experiences during OoT or ALttP, you'll know that I do get stuck, quite a bit. Whereas in TP, I was only 8 or 9, and used the guide for the first 2 dungeons, then did the rest by myself. From there, I might have gotten stuck at most, 5 times. But bare with me, I was only 8 or 9 and as a result, not half as skilled like I am now. TP is a 3 day trek for me now. OoT? Still not done! That alone is good enough reason.
I have played TP so many times I can almost play it with my eyes closed. OoT is definitely harder than TP. And by this I mean the endbosses are much harder. In TP none of the endbosses were hard to defeat. The endboss in Jabun Jabun, OoT alone took me longer to beat than Ganondorf in TP. OoT is not that hard but TP is really very easy to beat
Between OoT and TP? It would have to be OoT, hands down. The bosses were harder, as were the puzzles (The shifting climbing wall in the Spirit Temple always kicked my ***). I can't really remember getting stuck anywhere in TP, but then I get into the Water Temple in OoT and I get lost for a half an hour. Meanwhile, in TP I'm already riding the back of the dragon in the Ooccoo Temple (or whatever it's called. I don't really remember the name of the place, but I digress). There were many other difficult enemies in OoT as well. The giant hands from the ceiling-hell, the giant hands in GENERAL could drain you easily-especially the ones that mutiply. They're fun to fight.
I guess there are SOME challenges in TP, like finding all of the Poes. Yeah, I still haven't done that, unfortunately. Only 2 left! But then again, you had to find 100 Gold Skulltulas in OoT, and only 60 Poes in TP...
Whatever, anyway, OoT brought some more challenges in its puzzles, enemies, and bosses, more than TP ever brought. It's still a great game, but as far as a challenge, it's far outweighed by the competition.
I've been a lurker for a while and just registered today. I might view this differently than some since I played TP before OOT, but I don't think they seemed that different to me. In fact, when you consider that the first few dungeons in OOT were very easy (since it was the first 3-D game, I assume they went easy to get people used to the game), I have a hard time seeing OOT as harder overall. I do think certain things are harder in OOT, such as shooting arrows since there is no good target to shoot at like in the later games.