Why isn't there a large gap in the number of captured moons Jupiter and Saturn have?
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.