  We use new 144 MHz observations over 5634 deg$^2$ from the LOFAR Two-metre
Sky Survey (LoTSS) to compile the largest sample of uniformly-selected,
spectroscopically-confirmed quasars from the 14th data release of the Sloan
Digital Sky Survey (SDSS-DR14). Using the classical definition of
radio-loudness, $R=\log(L_{\rm{1.4GHz}}/L_{i})$, we identify 3,697 radio-loud
(RL) and 111,132 radio-quiet (RQ) sources at $0.6<z<3.4$. To study their
properties, we develop a new rest-frame spectral stacking algorithm, designed
with forthcoming massively-multiplexed spectroscopic surveys in mind, and use
it to create high signal-to-noise composite spectra of each class, matched in
redshift and absolute $i$-band magnitude. We show that RL quasars have redder
continuum and enhanced [OII] emission than their RQ counterparts. These results
persist when additionally matching in black hole mass, suggesting that this
parameter is not the defining factor in making a QSO radio-loud. We find that
these features are not gradually varying as a function of radio-loudness but
are maintained even when probing deeper into the RQ population, indicating that
a clear-cut division in radio-loudness is not apparent. Upon examining the star
formation rates (SFRs) inferred from the [OII] emission line, with the
contribution from AGN removed using the [NeV] line, we find that RL quasars
have a significant excess of star-formation relative to RQ quasars out to
$z=1.9$ at least. Given our findings, we suggest that radio-loud sources either
preferably reside in gas-rich systems with rapidly-spinning black holes, or
represent an earlier obscured phase of QSO evolution.
