Local genetic correlation evaluates the correlation of additive genetic effects between different traits across the same genetic variants at a genomic locus. It has been proven informative for understanding the genetic similarities of complex traits beyond that captured by global genetic correlation calculated across the whole genome. Several summary-statistics-based approaches have been developed for estimating local genetic correlation, including $\rho$-hess, SUPERGNOVA and LAVA. However, there has not been a comprehensive evaluation of these methods to offer practical guidelines on the choices of these methods. In this study, we conduct benchmark comparisons of the performance of these three methods through extensive simulation and real data analyses. We focus on two technical difficulties in estimating local genetic correlation: sample overlaps across traits and local linkage disequilibrium (LD) estimates when only the external reference panels are available. Our simulations suggest the likelihood of incorrectly identifying correlated regions and local correlation estimation accuracy are highly dependent on the estimation of the local LD matrix. These observations are corroborated by real data analyses of 31 complex traits. Overall, our findings illuminate the distinct results yielded by different methods applied in post-genome-wide association studies (post-GWAS) local correlation studies. We underscore the sensitivity of local genetic correlation estimates and inferences to the precision of local LD estimation. These observations accentuate the vital need for ongoing refinement in methodologies.