Despite progress in physical development and calibration, climate models still exhibit biases with respect to historical observations. As an alternative way to reduce them, run-time bias correction approaches have been developed, which consist in adding empirical tendency adjustment terms to the prognostic equations of some key physical variables. Although their ability to effectively reduce atmospheric circulation biases has been demonstrated, information is still missing regarding which method for estimating the adjustment terms is best suited for a given application. In this study, we implement a set of these methods in the atmospheric general circulation model LMDZ: nudging-based bias correction (the basis approach, a state-dependent version, and an iterative version), and the so-called climatological adaptive bias correction. Applying run-time bias correction on horizontal winds only, using these methods and varying some of their parameters, nine "bias-corrected versions'' of the model are created. They are evaluated using aggregate scores of global mean errors in circulation, temperature, and precipitation, as well as mid-latitude atmospheric variability features. A more regional perspective is also adopted, and a large region covering Europe and the North-Atlantic serves as a case study.  It is found that, when evaluated on global aggregate scores, some versions outperform others. We also show that this does not prejudge the outcome on mid-latitude atmospheric variability features or at regional scale. No strict recommendation can be made regarding the optimal methodological choice, and great caution is advised. The choice should be guided by the model user's needs and priorities.