Studies of radio-loud (RL) broad absorption line (BAL) quasars indicate that popular orientation-based BAL models fail to account for all observations. Are these results extendable to radio-quiet (RQ) BAL quasars? Comparisons of RL and RQ BAL quasars show that many of their properties are quite similar. Here, we extend these analyses to the rest-frame ultraviolet (UV) spectral properties, using a sample of 73 RL and 473 RQ BAL quasars selected from the Sloan Digital Sky Survey. Each RQ quasar is individually matched to an RL quasar in both redshift (over the range 1.5 < z < 3.5) and continuum luminosity. We compare several continuum, emission line, and absorption line properties, as well as physical properties derived from these measurements. Most properties in the samples are statistically identical, though we find slight differences in the velocity structure of the BALs that cause apparent differences in C iv emission line properties. Differences in the velocities may indicate an interaction between the radio jets and the absorbing material. We also find that UV Fe ii emission is marginally stronger in RL BAL quasars. All of these differences are subtle, so in general we conclude that RL and RQ BAL QSOs are not fundamentally different objects, except in their radio properties. They are therefore likely to be driven by similar physical phenomena, suggesting that results from samples of RL BAL quasars can be extended to their RQ counterparts.