© 2016 American Physical Society. We report a neutron spin-echo study of the critical dynamics in the S=52 antiferromagnets MnF2 and Rb2MnF4 with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the Néel temperature, TN. By taking advantage of the μeV energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents z for both longitudinal and transverse fluctuations. In MnF2, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents z in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb2MnF4, the critical dynamics crosses over from the expected 2D Heisenberg behavior for T TN to a scaling regime with exponent z=1.387(4), which has not been predicted by theory and may indicate the influence of long-range dipolar interactions.