We use new 144 MHz observations over 5634 deg2 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(L1.4GHz/Li), 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.