The new extremely large telescope projects need accurate evaluation of the candidate sites. In this paper, we present the astroclimatological comparison between the Paranal Observatory, located on the coast of the Atacama Desert (Chile), and the Observatorio del Roque de Los Muchachos (ORM), located in La Palma (Canary Islands). We apply a statistical analysis using long-term data bases from Paranal and Carlsberg Automatic Meridian Circle (CAMC) weather stations. The monthly, seasonal and annual averages of the main synoptical parameters in the two sites are computed. We compare the long-term trends in order to understand the main differences between the two sites. Significant differences between the two analysed sites have been found. Temperature has increasing trends in both observatories with somewhat higher evidence at the ORM. Seasonal variations of pressure at Paranal have been highly decreasing since 1989, and we do not see the same phenomenon at the ORM. The two sites are dominated by high pressure. In cold seasons, relative humidity (RH) is lower than 60 per cent at CAMC and 15 per cent at Paranal. In warm seasons, RH is lower than 40 per cent at CAMC and 20 per cent at Paranal. The analysis of the dew point has shown better conditions at Paranal with respect to CAMC in winter, autumn and spring before 2001, while the two sites are becoming similar afterwards. Winds at the ORM are subject to pronounced local variations.