We examine the Fundamental Plane of black hole activity for correlations with redshift and radio loudness in both radio-loud and radio-quiet quasar populations. Sources are compiled from archival data of both radio-loud and radio-quiet quasars over redshifts 0.1 < z < 5.0 to produce a sample of 353 sources with known X-ray, radio, and black hole mass measurements. A Fundamental Plane of accretion activity is fit to a sample of radio-loud and radio-quiet quasars, and we find a dichotomy between radio-loud and radio-quiet sources. The set of best-fitting equations that best describe the two samples are log LR = (1.12 +/- 0.06)logL_X_-(0.20 +/- 0.07)logM-(5.64 +/- 2.99) for our radio-loud sample and logL_R_ = (0.48 +/- 0.06)logL_X_ + (0.50 +/- 0.08)logM + (15.26 +/- 2.66) for our radio-quiet sample. Our results suggest that the average radio-quiet quasar emission is consistent with advection-dominated accretion, while a combination of jet and disc emission dominates in radio-loud quasars. We additionally examine redshift trends amongst the radio-loud and radio-quiet samples, and we observe a redshift dependence for the Fundamental Plane of radio-loud quasars. Lastly, we utilize the Fundamental Plane as a black hole mass estimation method and determine it useful in studying systems where standard spectral modelling techniques are not viable.