We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation DeltaF estimates as compared to other methods used in this report, while also offering rapid estimation of DeltaF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, "fast-growth" nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.