The N64 controller is the gamepad that introduced the analog stick to a generation. It's also the only mainstream controller in history with three handles, only one position you can comfortably hold at a time, and a notch on the underside that secretly fits a memory card.
What it gets right
The analog stick is the headline. It was the first commercial console pad to ship one, and Nintendo got it close enough to right that Super Mario 64 could exist. The Z-trigger underneath sat exactly where your middle finger expected, and stayed there for two console generations of "L1/L2/Z" arrangements before anyone questioned it.
The C-buttons on the right were used as a second control stick by most of the catalogue, years before dual-stick became a default expectation. Holding the right handle and using the C-buttons to look around in GoldenEye was the closest thing to modern aim-look that 1997 had.
What it gets wrong
The analog stick wears out. Nintendo's design used a plastic bowl rather than rubber, and over thousands of hours the bowl powders and the stick loosens. Replacement sticks are a small industry now.
The three-handle design forces a choice every time you pick it up. Most players settled on left-and-middle for analog games and left-and-right for D-pad games. A controller that needs you to relearn how to hold it for different titles is not a controller that aged well.
Worth keeping
For its catalogue, yes. The N64 library is small but specific, and most of it requires this controller to feel right. Mario Kart 64 with a Switch Pro Controller is an entirely different game.
Get the original grey, get a fresh stick, and use it for what it was designed for.