We analyze the common surface reflection and full-wave inversion methods to retrieve the soil surface dielectric permittivity and correlated water content from air-launched ground-penetrating radar (GPR) measurements. In the full-wave approach, antenna effects are filtered out from the raw radar data in the frequency domain, and full-wave inversion is performed in the time domain, on a time window focused on the surface reflection. Synthetic experiments are performed to investigate the most critical hypotheses on which both techniques rely, namely, the negligible effects of the soil electric conductivity (σ) and layering. In the frequency range 1--2 GHz we show that for σ > 0.1 Sm-1, significant errors are made on the estimated parameters, e.g., an absolute error of 0.10 in water content may be observed for σ = 1 Sm-1. This threshold is more stringent with decreasing frequency. Contrasting surface layering may proportionally lead to significant errors when the thickness of the surface layer is close to one fourth the wavelength in the medium, which corresponds to the depth resolution. Absolute errors may be >0.10 in water content for large contrasts. Yet we show that full-wave inversion presents valuable advantages compared to the common surface reflection method. First, filtering antenna effects may prevent absolute errors >0.04 in water content, depending of the antenna height. Second, the critical reference measurements above a perfect electric conductor (PEC) are not required, and the height of the antenna does not need to be known a priori. This averts absolute errors of 0.02--0.09 in water content when antenna height differences of 1--5 cm occur between the soil and the PEC. A laboratory experiment is finally presented to analyze the stability of the estimates with respect to actual measurement and modeling errors. While the conditions were particularly well suited for applying the common reflection method, better results were obtained using full-wave inversion.