Downscaling of Global Climate Model (GCM) outputs is essential to improve the reliability of climate projections at regional and local scales. This study presents a comparative analysis of two widely used statistical downscaling and bias correction methods—Quantile Mapping (QM) and Distribution Mapping (DM)—applied to rainfall and temperature data over the Sagar Division in central India. Daily observed rainfall data (1971–2005) from IMD gridded datasets and temperature data (1981–2005) from NASA-POWER were compared with downscaled outputs of two GCMs, ESM–2M and ESM–MR, at 0.5° × 0.5° resolution. Model performance was evaluated using statistical indices including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Nash–Sutcliffe Efficiency (NSE), and Kling–Gupta Efficiency (KGE). Results indicate that QM significantly improved the accuracy of rainfall simulations, with RMSE below 30 mm and NSE above 0.85, while DM performed poorly, yielding large errors (RMSE > 600 mm) and negative NSE values. Conversely, for temperature, DM achieved superior results, with RMSE < 0.3 °C and NSE > 0.96 for both maximum and minimum temperatures, whereas QM introduced higher residual errors. Between the two GCMs, ESM–MR consistently outperformed ESM–2M across variables. These findings emphasize the need for variable-specific bias correction approaches, suggesting QM for rainfall and DM for temperature in regional climate assessments.