Cross-scanner and cross-protocol variability of diffusion magnetic resonance imaging (dMRI) data are known to be major obstacles in multi-site clinical studies since they limit the ability to aggregate dMRI data and derived measures. Computational algorithms that harmonize the data and minimize such variability are critical to reliably combine datasets acquired from different scanners and/or protocols, thus improving the statistical power and sensitivity of multi-site studies. Different computational approaches have been proposed to harmonize diffusion MRI data or remove scanner-specific differences. To date, these methods have mostly been developed for or evaluated on single b-value diffusion MRI data. In this work, we present the evaluation results of 19 algorithms that are developed to harmonize the cross-scanner and cross-protocol variability of multi-shell diffusion MRI using a benchmark database. The proposed algorithms rely on various signal representation approaches and computational tools, such as rotational invariant spherical harmonics, deep neural networks and hybrid biophysical and statistical approaches. The benchmark database consists of data acquired from the same subjects on two scanners with different maximum gradient strength (80 and 300 mT/m) and with two protocols. We evaluated the performance of these algorithms for mapping multi-shell diffusion MRI data across scanners and across protocols using several state-of-the-art imaging measures. The results show that data harmonization algorithms can reduce the cross-scanner and cross-protocol variabilities to a similar level as scan-rescan variability using the same scanner and protocol. In particular, the LinearRISH algorithm based on adaptive linear mapping of rotational invariant spherical harmonics features yields the lowest variability for our data in predicting the fractional anisotropy (FA), mean diffusivity (MD), mean kurtosis (MK) and the rotationally invariant spherical harmonic (RISH) features. But other algorithms, such as DIAMOND, SHResNet, DIQT, CMResNet show further improvement in harmonizing the return-to-origin probability (RTOP). The performance of different approaches provides useful guidelines on data harmonization in future multi-site studies.