Winds in the outer part of the Red Spot reach 250 mph while the center remains quiescent. The striped cloud bands on Jupiter are not uniform. The striped pattern is divided into belts and zones. Winds flow first in one direction, then in the opposite direction. The cloud tops rise in a belt, and drop down in a zone.
Wind speeds blow east to west in a belt, and west to east in a zone.
There is no clear consensus yet on the details of why these bands, zones, and jets look the way they do. Therefore, we would expect the two planets to have somewhat different characteristics. The most obvious difference is that Jupiter is extremely colorful while Saturn is not. The primary reason these two planets look different has to do with the depth of their atmospheres. As mentioned, Jupiter is more massive.