This paper explores the performance of a pairwise differences estimator (PD) in the linear fixed effects models as an alternative to the fixed effects estimator (FE). Similar to FE, PD eliminates the unobserved fixed effects by data transformation but using a pairwise differencing approach instead of the mean-differencing. The main contribution of this paper is to show that PD generalizes FE by weighting each observation by its cluster size, and PD and FE are equivalent when 1) cluster sizes are equal or 2) local estimates of each cluster are equal. When PD and FE are distinct, a Monte Carlo simulation is designed to compare their performances in linear fixed effects models under different data settings. Both PD and FE produce accurate parameter estimates of the true value. For efficiency, PD provides valid improvements over FE in two restricted cases: 1) using the default i.i.d. standard errors in the homoscedastic panel data with the within-cluster error correlations being zero or very high; 2) using the cluster-robust standard errors in heteroscedastic clustered data with very high within-cluster regressor correlations and the number of clusters ranging from 6 to 10. In all other situations when the standard errors are valid, FE is a more efficient choice than PD.