To answer this properly, it's going to take a bit of writing, so I warn everyone now that walls of text are now in effect!
Gameplay: For the most part, I think we can all agree that the mapping of the controls was near flawless. In the remakes on the Gamecube system, as well as the Wii, nothing ever has beaten the sheer flawlessness of Z-targeting. For some reason, that centralized control stick just felt so naturally placed. With the rest of the controls neatly mapped to your right, for maximum efficiency, it didn't take long to flow easily from sword, to bow, to megaton hammer in the middle of a fight. Then you have your shield mapped to the bumper, which just makes things a whole lot easier. Main weapon > secondary weapons/tools > defense made a great layout across the controller.
As for the mechanics of the game, it revolutionized Zelda as we know it! You choose from THREE different tools, none of which had to include your sword. That brought a ton of options for puzzle solving, as well as fighting. Z-targeting brought about a slew of new options for fighting bosses in a 3-D environment that Super Mario 64 could only dream of. Backflips, side jumps, stabs, vertical and horizontal slashing and the leaping slash all pioneered more advanced techniques further along in the development of the serise. 3-D environments that allowed for the gagetry of Link to be used in brand new ways: the hookshot being able to transport you vertically, bows and boomerangs needing to be used against opponents swooping from above, you needed to strategically consider if Young Link's tools would be better or Old Link's tools would fit the bill; you got a horse GOD DAMNIT!!! All in all, gameplay took what rough edges SM64 had constructed and blew them out of the water with the dimensions OOT hit.
Graphics: Not much to be said here. Aside from the sheer vastness of Hyrule to explore in fully 3-D environments, there was a good mix of dynamics in each area. It brought about the need for some way to cross these expanses quickly, both in the form of teleportation to key spots and Epona for the rest. The graphics, for the period, were stunningly realistic, rather than the cartoony look that SM64 held (which is not a bad thing for Mario), which for most people seems to be a little more pleasing. Visual effects got a huge improvement, most evident when bosses attack or magic is used. Overall, the game just looked stunning.
Story: Now this is where SM64 starts to fall behind OOT by leaps and bounds. The story was told amazingly well. For a story that had been recycled a few times by this point, it was by far the best rendition. By the time the pieces started to fit together as to what was going on (past the point where you had advanced through time and became Old Link) you had already made serious emotional connections with the majority of the main cast. It's like going back to see your friends and family after being away for several years, only to find out everyone thought you were dead.
The unvierse is also much grittier than previous incarnations (with maybe the exception of LttP and the Dark World). Ganondorf is a power hungry monster put in a human's clothing where his villainous tendancies are brought to the forefront of his character development. He isn't "evil for the sake of evil" anymore. He has goals, which make him much scarier. But then so do the protagonists. The sages have thoughts and feelings much akin to the main villain that make you believe these people could exist. They aren't just a place holder for your quests to give you some tidbit of information about how Ganon is evil and you have to stop him. They want to stop him for their own, individual reasons. Saria wants to save the forests and keep Link's friends alive, Princess Ruto has a similar goal of keeping her people safe but also wants to marry Link, while Darunia (I think) wnats to restore the honour fo himself and his people. Maybe the goals resemble eachother in the whole "let's save the world" type of deal, but they clearly differ just enough to make them unique.
Overall, you need to consider that OOT is not a pioneer of 3-D gaming. Far from it. It is a Zelda title that came far after the last good Zelda title (LttP) that fans had been waiting for, it pulled it off in the most epic of ways and it made for a far more engaging game than SM64. This si why it'll be remembered as one of the greastest titles of its day!