We present time-of-flight differential cross section measurements and convergent close-coupling calculations of differential cross sections for the electron impact excitation of the X 1 Σ g + → b 3 Σ u + transition in molecular hydrogen. A part of this work was recently published in [Zawadzki et al. Phys. Rev. A 97, 050702(R) (2018)]. In this work, agreement between theory and experiment is excellent overall, and marks a transition in electron-molecule scattering where differential scattering of excitation is found to be in such precise agreement. We also present total electron impact excitation differential cross sections for H 2 for which agreement between theory and experiment is found to be excellent.