Which curve-fitting model should I use for my sigmoidal fit--the Boltzmann or one of the logistic equations?

The Boltzmann and "logistic" equations ("one site competition" or "sigmoidal dose-response") are equivalent, and will find the same best-fit curve. As implented in Prism, both expect X to be a logarithm. But the results are reported in different ways to follow the conventions of different fields. Boltzmann is traditionally used by electrophysiologists, while the others are used for dose-response and competitive binding data.