While Ocarina's successors on GameCube/Wii did naturally improve on its framerate and thus control responsiveness, I really feel that it wasn't until BOTW that another Zelda game managed to match the epic sense of adventure that made Ocarina so memorable and compelling.
I feel the same way, BotW captured a feeling I had not had since Ocarina. But there is one thing I would like to elaborate with that...
For me, Ocarina landed when I was around 10 years old. To 10 year old me playing the FIRST Legend of Zelda game that took place in a 3D space, and on top of that revolutionized the 3D gaming space itself as a while, it was the most epic feeling I had ever felt. But thats just it...it was 10 year old me experiencing something that was new and fresh, in a way none of us ever imagined. Sure I had played Zelda 1, 2, and ALttP...but taking the adventure to 3D space changed everything.
And that is why it FELT so epic. It does not mean WW, TP, or SS was any less of an epic adventure. But they were expanding and improving on something that we had all felt before. That fresh factor was missing. They used the formula that was established in ALttP, then took it into 3D space by expanding on Ocarina. That epic sense that you remember from Ocarina is more due to the timing of the game, rather than the game itself.
The reason BotW captured that, is because it took the formula and turned it up on its head. It was even far more open than Zelda 1, which still had limitations due to items and enemy strength. BotW took aspects of Zelda as well as blending them with aspects of other great games, and then put it all together in a way that had never been done before (or at least as effectively). It brought back that fresh feeling, and that is why it captures a similar feel of the epicness that Ocarina had during its time.