We studied the oscillator strength f of the band gap transition in heteronanocrystals (hNCs) with a spherical CdSe core embedded in an elongated CdS shell. A comparison with f of core-only CdSe NCs confirmed a reduction of the electron-hole overlap in hNCs with a band gap larger than 2.05 eV or smaller than 1.98 eV. However, the decrease in f is limited to about 50% when compared to CdSe NCs, suggesting that residual confinement still localizes the electron near the core. We correlated f with the radiative lifetime obtained from multiexponential photoluminescence (PL) decay traces. The different components were attributed to radiative decay, or deep and shallow carrier trapping, respectively, using the PL quantum efficiency (QE) as a guideline. Our data highlight the challenges associated when extracting the radiative decay, and demonstrate the added value of absorption spectroscopy to obtain the band-edge oscillator strength and the associated radiative recombination rate in colloidal hNCs.