Super Mario 64 might be the father of platformers, but an extremely compelling case can be made that Banjo-Kazooie is actually the best platform game for the N64, and one of the best Nintendo 64 games, period. The main characters alone make Banjo-Kazooie more fulfilling as they have actual personalities. In comparison, Mario said, "Wahoo!" when he jumped - end of character profile.
None of this is to suggest that Super Mario 64 wasn't a great game - it absolutely was and was absolutely revolutionary. But Banjo-Kazooie is too often viewed as a knock-off, and while it was inspired by the exploits of its Italian predecessor, it took the format to a whole new level. If only the two could have had a crossover, although Diddy Kong Racing (another great knock-off) offered something close to that by suggesting the two occupied the same universe.
Mario may stand atop the highest pedestal in the pantheon of video games, but here's why Banjo-Kazooie was the best version of the style innovated by the former. Be warned, after reading this you'll almost certainly have an irresistible urge to go buy Banjo-Kazooie, and maybe even a 64 if you don't have one, or yours can be revived with no amount of spittle-spewing blowing.
By the time Banjo-Kazooie came out, developer Rare had already made one of the greatest games of all time, GoldenEye 007, not to mention what they'd done with the Donkey Kong Country games on SNES (hint: they were great). So Rare already had the full faith of gamers, and when it was announced that they'd be making a 3D platformer à la Super Mario 64, people went nuts. Mario 64 was great, but what could such an accomplished developer do with that format? The answer, in short: wonders.
One didn't simply walk through automated doors once the requisite stars were collected in Banjo-Kazooie. To enter a world the player might have to jump into a giant treasure chest or an animate (and adorable) cauldron. These are small differences, but they make a world of difference. What's more, the central hub, which the player had to navigate to find these different worlds, held its own secrets. Yes, Mario 64 had a secret passage or two in the castle, but Grunty's Lair was replete with puzzles and secrets - it was so much more than a vessel or nexus where the entrances to other lands resided. And these lands had so much more personality than those of Mario. While Mario's world were really just 3D versions of the original game, the worlds of Banjo-Kazooie had so much character they were almost characters themselves.
Click-Clock Wood was a world that had four different representations, one for each season, that the player had to navigate. Actions in one season would affect those of another, requiring the player to explore the interconnectedness to achieve everything within, like planting a seed in spring only to come back and find a fully grown flower in the fall with a puzzle piece on top. Each season you can enter Nabnut the squirrel's house to find various collectibles, or complete the task he only offers in autumn, or return for a final collectible in winter to find Nabnut passed out in bed with a lady squirrel. The whimsically named Gnawty the beaver is another NPC indigenous to the area, and just another example of what made the game dynamic.
Banjo-Kazooie took Mario 64's "open world platformer" concept to a whole new level. Click-Clock Wood was the ninth world of the game and was, again, essentially four worlds in one. Each land was significantly larger than Mario's individual worlds, and the player had to revisit them as they gained new abilities throughout the game, expanding the life of each place. Banjo-Kazooie was as close to an RPG as a platformer could get.