I love the exploring, collecting, learning moves aspect of Banjo Kazooie and 3D platformers, but I think a core facet that some people fail to understand is that Banjo Kazooie was a LOT more than just collecting items to open doors and learn skills. Or at least, I think people understand it, but don't pay attention to it.
Banjo Kazooie for me is a cohesive, charming, hilarious universe. The bright colors, nonsense speech, brilliant thematic worlds and characters created an experience that took the game far beyond just collecting and jumping. Banjo Kazooie and Tooie just absolutely ooze charm and wonder. And on top of that the characters interact with each other in really meaningful ways. You really feel that Banjo and Kazooie are friends who sometimes lightly jab at each other. And the NPCs have the same level of attention. Every single character has, well, character! I wanted to know more about these characters. I looked forward to seeing what Bottles, Jamjars, Gobi, Grunty and her sisters, King Jingaling, etc. will say next. Even on the N64 they had well-developed personalities and motivations. Even Bullion Bill who was barely in the game was interesting.
AND THE SECRETS! Stop N' Swop added an entire additional layer of wonder, keeping me hooked long after I 100%d the game. And the Mega Glowbo adventure in Banjo Tooie. Finding these little easter eggs was awesome! And the secret puzzles in Banjo's house. Becoming a washing machine. I mean seriously, how great were those games!?
I love the 3D platforming and collecting (I played DK64, Jak & Daxter, Ratchet and Clank, etc) but the characters and feel of the world is what really sets these games apart, for me.
Edit: And the music. I mean, you can't strip that away. Every portion of the experience adds up to what makes it a fantastic game. It's the whole that matters, even though the parts are also great. You wouldn't take bass and cellos out of a symphony and expect the same end result.
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