The purpose of this study is to compare the performance of prediction models based either on the bulk optical properties (BOP) or with models based on the diffuse reflection and transmission spectra to assess the soluble solids content (SSC) or fruit firmness (FF) of ‘Fuji’ apples. Diffuse reflection and transmission spectra of 240 apples in 500–1000 nm were acquired using a self-constructed single integrating sphere system, from which the absorption coefficient (μa) and reduced scattering coefficient (μ′s) were determined. The relationships of μa, μ′s, and the reflection and transmission spectra with the SSC and FF were analyzed, and detection models were established using partial least squares regression coupled with characteristic wavelength selection. Results showed that neither the SSC nor the FF changed obviously during 80-days storage, and the μa and μ′s showed no monotonic increase or decrease pattern. The SSC prediction model based on μa spectra combined with the baseline correction method performed the best (R2p = 0.79, RMSEP = 0.62), while the model based on μ′s spectra was the best for FF (R2p = 0.67, RMSEP = 0.35 N). Overall, the accuracy of the model based on BOP in predicting internal quality was better than that based on reflection and transmission spectra from the same measurement. •BOP, reflection and transmission spectra of apples were acquired from the same measurement.•Changes of SSC, FF, reflectance, transmittance and BOP during storage were analyzed.•PLSR models of SSC and FF based on BOP were compared with those based on spectra.•Absorption and scattering properties performed the best for SSC and FF prediction.•Quality evaluation based on BOP was superior to reflection and transmission spectra.