LOPES is a digital antenna array for the radio measurement of cosmic-ray air showers at energies around 1017 eV. It is triggered by the KASCADE-Grande air-shower array at the Karlsruhe Institute of Technology (KIT), Germany. Because of an absolute amplitude calibration and a sophisticated data analysis, LOPES can test models for the radio emission to an up-to-now unachieved level, thus improving our understanding of the radio emission mechanisms. Recent REAS simulations of the air-shower radio emission come closer to the measurements than any previously tested simulations. We have determined the radio-reconstruction precision of interesting air-shower parameters by comparing LOPES reconstructions to both REAS simulations and KASCADE-Grande measurements, and present our latest results for the angular resolution, the energy and the Xmax reconstruction based on the radio measurement of about 500 air showers. Although the precision of LOPES is limited by the high level of anthropogenic noise at KIT, it opens a promising perspective for next-generation radio arrays in regions with a lower ambient noise level.