We present the results of a radio and X-ray study of the Galactic microquasar GRS 1758-258, using unpublished archival data and new observations. We focus in particular on the 2000-2002 state transitions, and on its more quiet behaviour in 2008-2009. Our spectral and timing analysis of the XMM-Newton data shows that the source was in the canonical intermediate, soft and hard states in 2000 September 19, 2001 March 22 and 2002 September 28, respectively. We estimate the disk size, luminosity and temperature, which are consistent with a black hole mass ~10 M_{sun}. There is much overlap between the range of total X-ray luminosities (on average ~0.02 L_{Edd}) in the hard and soft states, and probably between the corresponding mass accretion rates; in fact, the hard state is often more luminous. The extended radio lobes seen in 1992 and 1997 are still present in 2008-2009. The 5-GHz radio core flux density has shown variability between ~0.1-0.5 mJy over the last two decades. This firmly places GRS 1758-258 in the radio-quiet sequence of Galactic black holes, in the radio/X-ray plane. We note that this dichotomy is similar to the dichotomy between the radio/X-ray sequences of Seyfert and radio galaxies. We propose that the different radio efficiency of the two sequences is due to relativistic electron/positron jets in radio-loud black holes, and sub-relativistic, thermally dominated outflows in radio-quiet sources. ; Comment: 17 pages, 1.6 MB, accepted by MNRAS