Context: The origin of broad-absorption-line quasi-stellar objects (BAL QSOs) remains unclear. Accounting for ∼20% of the QSO population, these objects have broad absorption lines in their optical spectra generated from outflows with velocities of up to 0.2 c. In this work, we present the results of a multi-frequency study of a well-defined radio-loud BAL QSO sample, and a comparison sample of radio-loud non-BAL QSOs, both selected from the Sloan Digital Sky Survey (SDSS).Aims: We aim to test which of the currently popular models of the BAL phenomenon - "orientation" or " evolutionary" - best accounts for the radio properties of BAL quasars. We also consider a third model in which BALs are produced by polar jets driven by radiation pressure. Methods: Observations from 1.4 to 43 GHz have been obtained with the VLA and Effelsberg telescopes, and data from 74 to 408 MHz have been compiled from the literature. The spectral indices give clues about the orientation, while the determination of the peak frequency can constrain the age, and test the evolutionary scenario, in which BAL QSOs are young QSOs. The fractional polarisation and the rotation measure in part reflect the local magnetic field strength and particle density. Results: The fractions of resolved sources in the BAL and non-BAL QSO samples are similar (16% versus (vs.) 12%). The resolved sources in the two samples have similar linear sizes (20 to 400 kpc) and morphologies. There is weak evidence that the fraction of variable sources amongst BAL QSOs is smaller. The fractions of candidate GHz-peaked sources are similar in the two samples (36 ± 12% vs. 23 ± 8%), suggesting that BAL QSOs are not generally younger than non-BAL QSOs. Both BAL and non-BAL QSOs have a wide range of spectral indices, including flat-spectrum and steep-spectrum sources, consistent with a broad range of orientations. There is weak evidence (91% confidence) that the spectral indices of the BAL QSOs are steeper than those of non-BAL QSOs, mildly favouring edge-on orientations. At a higher level of significance (≥97%), the spectra of BAL QSOs are no flatter than those of non-BAL QSOs, which suggests that a polar orientation is not preferred. The distributions of fractional polarisation in the two samples have similar median values (1-3%). The distributions of rotation measure are also similar, the only outlier being the BAL QSO 1624+37, which has an extreme rest-frame rotation measure (from the literature) of -18 350 ± 570 rad m-2.