  We cross-correlate the SDSS DR3 quasar sample with FIRST and the Vestergaard
et al. black hole (BH) mass sample to compare the mean accretion histories of
optical and radio quasars. We find significant statistical evidence that radio
quasars have a higher mean Eddington ratio Lambda at z > 2 with respect to
optical quasars, while the situation is clearly reverse at z < 1. At z > 2
radio quasars happen to be less massive than optical quasars; however, as
redshift decreases radio quasars appear in increasingly more massive BHs with
respect to optical quasars. These two trends imply that radio sources are not a
mere random subsample of optical quasars. No clear correlation between radio
activity and BH mass and/or accretion rate is evident from our data, pointing
to other BH properties, possibly the spin, as the driver of radio activity. We
have checked that our main results do not depend on any evident bias. We
perform detailed modelling of reasonable accretion histories for optical and
radio quasars, finding that radio quasars grow by a factor of a few, at the
most, since z ~ 4. The comparison between the predicted mass function of active
radio quasars and the observed optical luminosity function of radio quasars,
implies a significantly lower probability for lower mass BHs to be radio loud
at all epochs, in agreement with what is observed in the local universe.
