In this work we perform a neutron Bragg edge tomography of stainless steel 316L additive manufacturing samples, one as built via standard laser powder bed fusion, and one using the novel three-dimensional (3D) laser shock peening technique. First, we consider conventional attenuation tomography of the two samples by integrating the signal for neutron wavelengths beyond the last Bragg edge, to analyze the bulk density properties of the material. This is used to map defects, such as porosities or cracks, which yield a lower density. Second, we obtain strain maps for each of the tomography projections by tracking the wavelength of the strongest Bragg edge corresponding to the {111} lattice plane family. Algebraic reconstruction techniques are used to obtain volumetric 3D maps of the strain in the bulk of the samples. It is found that not only the volume of the sample where the shock peening treatment was carried out yields a higher bulk density, but also a deep and remarkable compressive strain region. Finally, the analysis of the Bragg edge heights as a function of the projection angle is used to describe qualitatively crystallographic texture properties of the samples.