We present our broadband (2 -250 keV) time-averaged spectral analysis of 388 bursts from SGR J1550−5418, SGR 1900+14 and SGR 1806−20 detected with the Rossi X-ray Timing Explorer (RXTE) here and as a database in a companion web-catalog. We find that two blackbody functions (BB+BB), sum of two modified blackbody functions (LB+LB), sum of blackbody and powerlaw functions (BB+PO) and a power law with a high energy exponential cut-off (COMPT) all provide acceptable fits at similar levels. We performed numerical simulations to constrain the best fitting model for each burst spectrum and found that 67.6% burst spectra with well-constrained parameters are better described by the Comptonized model. We also found that 64.7% of these burst spectra are better described with LB+LB model, which is employed in SGR spectral analysis for the first time here, than BB+BB and BB+PO. We found a significant positive lower bound trend on photon index, suggesting a decreasing upper bound on hardness, with respect to total flux and fluence. We compare this result with bursts observed from SGR and AXP sources and suggest the relationship is a distinctive characteristic between the two. We confirm a significant anti-correlation between burst emission area and blackbody temperature and find that it varies between the hot and cool blackbody temperatures differently than previously discussed. We expand on the interpretation of our results in the framework of strongly magnetized neutron star case.