Increasing knowledge on wind shear models to strengthen their reliability appears as a crucial issue, markedly for energy investors to accurately predict the average wind speed at different turbine hub heights, and thus the expected wind energy output. This is particularly helpful during the feasibility study to abate the costs of a wind power project, thus avoiding installation of tall towers, or even more expensive devices such as LIDAR or SODAR. The power law (PL) was found to provide the finest representation of wind speed profiles and is hence the focus of the present study. Besides commonly used for vertical extrapolation of wind speed time series, the PL relationship between "instantaneous" wind profiles was demonstrated by Justus and Mikhail to be consistent with the height variation of Weibull distribution. Therefore, in this work a comparison is performed between these two different PL-based extrapolation approaches to assess wind resource to the turbine hub height: (i) extrapolation of wind speed time series, and (ii) extrapolation of Weibull wind speed distribution. The models developed by Smedman-Högström and Högström (SH), and Panofsky and Dutton (PD) were used to approach (i), while those from Justus and Mikhail (JM) and Spera and Richards (SR) to approach (ii). Models skill in estimating wind shear coefficient was also assessed and compared. PL extrapolation models have been tested over a flat and rough location in Apulia region (Southern Italy), where the role played by atmospheric stability and surface roughness, along with their variability with time and wind characteristics, has been also investigated. A 3-year (1998-2000) 1-h dataset, including wind measurements at 10 and 50 m, has been used. Based on 10-m wind speed observations, the computation of 50-m extrapolated wind resource, Weibull distribution and energy yield has been made. This work is aimed at proceeding the research issue addressed within a previous study, where PL extrapolation models were tested and compared in extrapolating wind resource and energy yield from 10 to 100 m over a complex-topography and smooth coastal site in Tuscany region (Central Italy). As a result, wind speed time series extrapolating models proved to be the most skilful, particularly PD, based on the similarity theory and thus addressing all stability conditions. However, comparable results are returned by the empirical JM Weibull distribution extrapolating model, which indeed proved to be preferable as being: (i) far easier to be used, as z0-, stability-, and wind speed time series independent; (ii) more conservative, as wind energy is underpredicted rather than overpredicted.