Why does Saturn have a more prominent equatorial bulge and higher flattening ratio than Jupiter despite rotating slower? It is my understanding that a planet's equatorial bulge is caused by the centrifugal force produced by its rotation, and the faster a planet rotates the bigger the bulge and flattening ratio of a planet is. 

Jupiter's rotational period is 9.925 hours while Saturn's is 10.56 hours. However, Saturn not only has a higher flattening ratio than Jupiter, but also has a bigger equatorial bulge (11,801 km vs. 9,276 km) despite rotating slower and being smaller. Am I missing something?
Consider the dimensionless parameter $k$ for some planet, given by
$$k \equiv \frac{\Omega^2 a^3}{G M}$$
where


$\Omega$ is the planet's equatorial sidereal rotation rate,
$a$ is the planet's equatorial radius,
$G$ is the universal gravitational constant, and
$M$ is the planet's mass.


The values for this dimensionless parameter are


0.003461 for the Earth,
0.08919 for Jupiter, and
0.1576 for Saturn.


The factor $k$ is essentially the ratio of centrifugal effects to gravitational effects at the "surface" at the equator of the planet, surface in scare quotes because giant planets don't quite have a surface. Ignoring higher order terms, the flattening of a uniform density planet in hydrostatic equilibrium can be shown to be $\frac54k$. The mathematics that go into this derivation are a bit hairy, even for a planet of uniform density, so for now I'll just state this as a fact. (But see Rotational Flattening, for example. Note well: The derivation at this site involves a bit of hand-waving. Overcoming the hand-waving involves even more mathematics.)

The assumption of uniform density is not that good. Even if one does allow for density variations as a function of radial distance from the center of the planet, the parameter $k$ defined above plays a significant role in the computation of what the flattening should be. The observed flattening of Saturn versus that of Jupiter is consistent with the fact that the value of $k$ for Saturn is 1.76 times that of the value for Jupiter.