The N64's third party support was crap for largely the same reason the Wii's was. But Nintendo's first party output was never stronger. I think the SNES is Nintendo's best system but the strong third party support is part of that. The best games on the N64 are virtually all Nintendo games. Super Mario 64, Goldeneye, Star Fox 64, Banjo-Kazooie, Ocarina of Time, Super Smash Bros., Perfect Dark, Majora's Mask, F-Zero X, Paper Mario, Conker's Bad Fur Day... should I go on?
The N64 had lousy third party support but it was like Nintendo KNEW they had to support the system themselves and stepped up to the plate. When you're it, you have to try to deliver with every game. Nintendo's Cube and Wii output feels more like the sort of output Nintendo would have done if they had good third party support. It's like they just pretended the third party support was fine and continued on their way. On the N64 it really felt like they were busting their ass trying to fill the void. "Quality over quantity" is just PR speak but if there was ever a time where you might think Nintendo tried to fulfill that, the N64 was it.
The switch to 3D really helped. They pretty much got to reboot every one of their existing franchises. I feel like a lot of Nintendo's older franchises started to feel stale during the Cube era. Sequels are easier to do early in a series. You can put in the ideas that were left on the cutting room floor into your sequels. In those days the hardware boosts also helped. A Link to the Past and Super Metroid get praise for being some of the greatest games ever. But how else would you make those games? They have the exact enhancements over the NES games one would expect from the new options the SNES would provide.
The N64 had that more than any system because of the switch to 3D. It was obvious that Mario 64 wouldn't just be Super Mario World Part 2. The polygons are there so they're going to use them. Each sequel could be approached with "now in 3D!" Though that era was full of failed transitions from 2D to 3D. Nintendo was probably the only company to NEVER **** any of them up. That took talent and creativity and very careful design. That was a tremendous achievement. And it allowed every sequel to feel really fresh and new. One of my favourite Cube games is Metroid Prime and because there was no N64 Metroid it got the same "instant freshness" the rest of Nintendo's franchises got, only a generation later.
On the Cube there were times where it seemed like Nintendo knew they had built up a reputation as the guys that make each sequel count and stand out, but the new ideas were not so obvious as they were in previous generations. So we got stuff like the water pack in Mario and two man karts in Mario Kart and toon shading in Zelda. They needed to be creative and innovative so they came up with kind of lame, forced ideas. And then you get the Wii where the whole CONSOLE is a forced idea as the typical hardware upgrade did not have such obvious advantages that previous console generations offered. For Nintendo is went rough 2D->polished 2D->rough 3D->polished 3D->
Uh, motion control I guess? Now let's try a tablet controller? The obvious upgrade doesn't exist anymore for both hardware and existing Nintendo franchises. This is why I suggest they create new IP because that's the best way for them to offer new and fresh gameplay experiences. It isn't like the N64 gen where they can take all their existing IP and apply the same general update to all of them.
Though since the N64 is the "rough 3D" generation a lot of the games can be hard to look at now and have some wonky framerates. Gamecube and Wii games are typically more polished, they just lack the genre-changing impact of the N64 games. I think for a younger gamer there is a certain "you had to be there" factor. OoT isn't specifically better than TP, it's just that OoT was groundbreaking stuff at the time and TP in comparison was very conventional.