Zonal flow on Jupiter and Saturn consists of equatorial super–rotation and alternating East-West jet streams at higher latitudes. Interacting with these zonal flows, numerous vortices occur with various sizes and lifetimes. The Juno mission and Cassini’s grand finale have shown that the zonal jets of Jupiter and Saturn extend deeply into their molecular envelopes. On Jupiter, the vast majority of low and mid-latitude jovian vortices are anticyclonic, whereas cyclones appear at polar latitudes. Cassini mission observations revealed a similar pattern on Saturn; its North and South polar vortices are cyclonic, whereas anticyclones occur at mid-latitudes. We use the recently developed code Rayleigh to run high-resolution simulations of rotating convection in 3D spherical shells. Four model runs are presented that result in dynamical flows that are comparable to those on the giant planets. We confirm previous results, finding that deep convective turbulence can explain the structure of jets. However, the strength and depth of stable stratification, and the latitude, can modify jet morphologies and affect the formation and dynamics of vortices. Lower latitudes favour shallow anticyclonic vortices that form due to upward and divergent flow near the outer boundary. These anticyclones are typically shielded by cyclonic filaments associated with downwelling return flow. In contrast, a single polar cyclone, or clusters of cyclones form near the poles. All of our simulations have this global pattern; a strong preference for shallow anticyclones in the first anticyclonic shear zone away from the equatorial jet (corresponding to the region of the great red spot on Jupiter and Storm Alley on Saturn), cyclonic and anticyclonic vortices at higher mid-latitudes, and a deeply seated cyclone or cyclone clusters at each pole. Our results show that Juno and Cassini observations of cloud-level flow can be explained in terms of deep convective dynamics in the molecular envelopes of Jupiter and Saturn.