With the sample of observed tidal disruption events (TDEs) now reaching several tens, distinct spectroscopic classes have emerged: TDEs with only hydrogen lines (TDE-H), only helium lines (TDE-He), or hydrogen in combination with He ii and often N iii/O iii (TDE-H + He). Here, we model the light curves of 32 optically bright TDEs using the Modular Open Source Fitter for Transients (mosfit) to estimate physical and orbital properties, and look for statistical differences between the spectroscopic classes. For all types, we find a shallow distribution of star masses, compared to a typical initial mass function, in the range similar to 0.1-1 M-circle dot, and no TDEs with very deep encounters. Our main result is that TDE-H events appear to come from less complete disruptions (and possibly lower SMBH masses) than TDE-H+He, with TDE-He events fully disrupted. We also find that TDE-H events have more extended photospheres, in agreement with recent literature, and argue that this could be a consequence of differences in the self-intersection radii of the debris streams. Finally, we identify an approximately linear correlation between black hole mass and radiative efficiency. We suggest that TDE-H may be powered by collision-induced outflows at relatively large radii, while TDE-H + He could result from prompt accretion discs, formed more efficiently in closer encounters around more massive SMBHs.