We present X-ray spectral and long-term variability analyses of an unbiased sample of 361 optically selected radio-loud quasars (RLQs) utilizing sensitive serendipitous X-ray data from the Chandra and XMM-Newton archives. The spectral and temporal properties of RLQs are compared with those of radio-quiet quasars (RQQs) matched in L2500 {AA} and z. The median power-law photon index ({gamma}) of RLQs is 1.84_-0.01_^+0.01^, which is close to that of matched RQQs (1.90_-0.01_^+0.02^). No significant correlations between {gamma} and radio-loudness, Lx/L_x,rqq_ (the X-ray luminosity over that expected from the Lx-Luv relation for RQQs), redshift, or Eddington ratio are found for our RLQs. The stacked X-ray spectra of our RLQs show strong iron-line emission and a possible Compton-reflection hump. The intrinsic X-ray variability amplitude is ~= 40 per cent for RLQs on time-scales of months-to-years in the rest frame, which is somewhat smaller than for the matched RQQs (~= 60 per cent) on similar time- scales, perhaps due to the larger black hole masses and lower Eddington ratios in our RLQ sample. The X-ray spectral and variability results for our RLQs generally support the idea that the X-ray emission of typical RLQs is dominated by the disc/corona, as is also indicated by a recent luminosity correlation study.