Why isn't there a large gap in the number of captured moons Jupiter and Saturn have? Given that Jupiter is roughly 3x as massive compared to Saturn and is located right next to the asteroid belt, it feels that Jupiter should easily have a larger amount of captured moons. However currently, due to a recent survey of Saturn discovering 20 new moons, Saturn has 57 observed captured moons compared to Jupiters 71. 

Also summing the mass of the 6 largest captured moons for each planet gives:
- Jupiter: 7.844*10^18kg
- Saturn: 8.372*10^18kg

Why isn't there a larger gap between the number and mass of Jupiter and Saturns captured moons?

Note:
While Jupiter has a very large amount of Trojan asteroids, the main focus of the question is moons directly in orbit around the main planet.
Gravitational mass is not the be-all and end-all. Two other metrics are the Hill sphere and gravitational sphere of influence. These are widely used metrics that describe the volume over which a planetary body dominates gravitationally over than of the Sun. Saturn has a larger Hill sphere and a larger gravitational sphere of influence than does Jupiter.

This suggests that Saturn might have many more moons than does Jupiter. Saturn's much greater distance from the Sun compared to Jupiter's suggests that discovering a new Saturnian moon is over three times harder than is discovering a new comparably sized Jovian moon. This might be why the ratio is as close as it is.