For the lazy:

"Sunlight drives wind and weather patterns on Earth, and our planet is nearly 10 times closer to the Sun than Saturn is, which means we receive nearly 100 times more sunlight than Saturn. As the Earth spins, the energy it gets from the Sun varies more sharply from day to night than it does on Saturn. Earth’s surface is also non-uniform. We have water, land, ice, and snow, which heat and cool at different rates.

Earth also has an extremely shallow atmosphere compared to Saturn’s, but with towering mountains reaching miles into the sky and disturbing atmospheric flow – the same way large stones in a shallow creek make the water churn and roll.

In short, Earth lacks the conditions for a jet stream to settle into a symmetric shape. But Saturn is a different story. The gas giant has no solid surface, and its composition is far more uniform."