Context : Most X-ray studies of broad absorption line quasars ( BALQSOs ) found significant ( N _ { H } \sim 10 ^ { 22 - 24 } cm ^ { -2 } ) intrinsic column densities of gas absorbing an underlying typical power-law continuum emission , in agreement with expectations from radiatively driven accretion disk wind models . However , direct spectral analysis was performed only on a limited number of bright sources . Aims : We investigate the X-ray emission of a large number of BALQSOs at medium to high redshift ( 0.8 \lesssim z \lesssim 3.7 ) with the best data available to date . Methods : We drew a large BALQSO sample from the cross-correlation of SDSS DR5 and 2XMM catalogs to perform moderate-quality X-ray spectral and hardness ratio analysis and X-ray/optical photometry . We compare our results with previous studies of BALQSOs and theoretical disk wind model expectations . Results : No or little intrinsic X-ray neutral absorption is found for one third of the spectroscopically analyzed BALQSO sample ( N _ { H } < 4 \times 10 ^ { 21 } \ > cm ^ { -2 } at 90 % confidence level ) , and lower than typical X-ray absorption is found in the remaining sources ( \langle N _ { H } \rangle \sim 5 \times 10 ^ { 22 } \ > cm ^ { -2 } ) even including the faintest sources analyzed through hardness ratio analysis . The mean photon index is \Gamma \sim 1.9 , with no significant evolution with redshift . The optical/X-ray spectral indices \alpha _ { ox } are typical of radio-quiet broad line AGN , in contrast with the known ( from previous X-ray studies ) “ soft X-ray weakness ” of BALQSOs and in agreement with the lack of X-ray absorption . We found the low-absorption index ( AI ) subsample to host the lowest X-ray absorbing column densities of the entire sample . Conclusions : X-ray selected BALQSOs show lower X-ray absorption than purely optically selected ones , and soft X-ray weakness does not hold for any of them . Their outflows may be launched by different mechanisms than classical soft X-ray weak BALQSOs or they may be the tail of the already known population seen along a different line of sight , in both cases expanding the observational parameter space for their search and investigation .