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Pre-scission and post-scission neutron yields have been measured as a function of projectile mass, compound nucleus fissility, and fission mass split and total kinetic energy (TKE) for 27 fusion-fission and quasifission reactions induced by beams of $^{16,18}\mathrm{O}$, $^{40}\mathrm{Ar}$, and $^{64}\mathrm{Ni}$. A new method of interpretation of experimental pre-scission neutron multiplicities ${\ensuremath{\nu}}_{\mathrm{pre}}$ and mean kinetic energies ${\mathrm{\ensuremath{\varepsilon}}}_{\ensuremath{\nu}}$ allows the extraction of fission time scales with much less uncertainty than previously, all fusion-fission results being consistent with a dynamical time scale of (35\ifmmode\pm\else\textpm\fi{}15)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}21}$ s for symmetric fission. All reactions show that ${\ensuremath{\nu}}_{\mathrm{pre}}$ falls quite rapidly with increasing mass asymmetry; evidence is presented that for fusion-fission reactions this is partly due to a reduction of the dynamical fission time scale with mass asymmetry. For quasifission, the data indicate that the pre-scission multiplicity and mean neutron kinetic energy are very sensitive to the final mass asymmetry, but that the time scale is virtually independent of mass asymmetry. It is concluded that for fusion-fission there is no dependence of ${\ensuremath{\nu}}_{\mathrm{pre}}$ on TKE, while for $^{64}\mathrm{induced}$ quasifission reactions, a strong increase of ${\ensuremath{\nu}}_{\mathrm{pre}}$ with decreasing TKE is observed. This is probably largely caused by neutron emission during the acceleration time of the fission fragments in these fast reactions. Interpretation of post-scission multiplicities in terms of fragment excitation energies leads to deduced time scales consistent with those determined from the pre-scission data.