We demonstrate the advantages of spherical convolutional neural networks over conventional fully connected networks at estimating rotationally invariant microstructure indices. Fully-connected networks (FCN) have outperformed conventional model fitting for estimating microstructure indices, such as FA. However, these methods are not robust to changes diffusion weighted image sampling scheme nor are they rotationally equivariant. Recently spherical-CNN have been supposed as a solution to this problem. However, the advantages of spherical-CNNs have not been leveraged. We demonstrate both spherical-CNNs robust to new gradient schemes as well as the rotational equivariance. This has potential to decrease the number of training datapoints required.