The neutron spectra and ambient dose equivalent were determined by unfolding measured Bonner sphere system data using different unfolding methods. These methods included a maximum entropy method (MAXED code), nonlinear least-squares method (GRAVEL code) with several different starting spectra, and a genetic algorithm method. These algorithms were used to unfold measured Bonner sphere data that had been collected using a LiI(Eu) detector and activation foils. The Bonner sphere system was exposed to neutrons from a known AmBe source and at the proton accelerator facility at the University of Texas M. D. Anderson Cancer Center. The total fluence rates and total ambient dose equivalents of the neutron field agree within 7.5%, regardless of unfolding algorithm or starting spectrum. In contrast, the fluence-weighted average energy varied dramatically, depending on the starting spectrum used in the unfolding process. These findings offer insight and guidance into the use of unfolding algorithms and starting spectra for neutron spectroscopy.