Several models for physics beyond the Standard Model predict new particles with a decay signature including hard photons and missing energy. Two well-motivated examples are supersymmetry with gauge-mediated breaking (GMSB) and the standard model with two universal extra dimensions. Both models lead to decay chains with similar collider signatures, including hard photon emission. The main discriminating feature are the spins of the new particles. In this paper we discuss how information about the spins of the particles can be extracted from lepton-photon or quark-photon invariant mass distributions at the Large Hadron Collider. The characteristic shapes of the distributions are derived analytically and then studied in a realistic Monte-Carlo simulation. We find that for a typical GMSB mass spectrum with particle masses below 1 TeV, already 10 fb−1 integrated luminosity at 14 TeV center-of-mass energy are sufficient to discriminate the two models with high significance.