We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the Planck 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, H0 measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and ΛCDM models, using the Savage-Dickey method. We find that the RT model and ΛCDM perform equally well, while the RR model is disfavored.