In this work, we evaluate the performance of three different diffusion MRI (dMRI) signal representations in the estimation of brain microstructural indices in combination with fully connected neural networks (FC-NN). The considered signal representations are the raw samples on the sphere, the spherical harmonics coefficients, and a novel set of recently presented rotation invariant features (RIF). To train FC-NN and validate our results, we create a synthetic dMRI dataset that mimics the signal properties of brain tissues and provides us a real ground truth for our experiments. We test 8 different network configurations changing both the depth of the networks and the number of perceptrons. Results show that our new RIF are able to estimate the brain microstructural indices more precisely than the diffusion signal samples or its spherical harmonics coefficients in all the tested network configurations. Finally, we apply the best-performing FC-NN in-vivo on a healthy human brain.