Ground layer Adaptive Optics (GLAO) is a new variant of adaptive optics that aims at correcting the seeing over a wide field of view by conjugating the deformable mirror to the boundary layer altitude.The South Pole is expected to be particularly to GLAO due to the absence of high altitude jets and the confinement of 96% of the seeing within a 220 m boundary layer. We present here the comparison of a GLAO system on a 2 m class infrared telescope at the South Pole and at Paranal. Our results, which show that the two sites obtain similar performance, are derived analytically using the simulation tool PAOLA (Performance of Adaptive Optics for Large Apertures).