This article presents a comprehensive analysis of the performance prospects of double-drift region (DDR) impact avalanche transit time (IMPATT) oscillators fabricated using wide-bandgap (WBG) semiconductor materials, particularly cubic silicon carbide (3C-SiC) and type-IIb diamond, for use in the millimeter-wave (mm-wave) and terahertz (THz) frequency bands. The study contrasts these advanced material-based devices with traditional silicon (Si) DDR IMPATT oscillators to highlight the advantages offered by WBG materials in high-frequency solid-state (radiofrequency) RF generation. A non-sinusoidal voltage excitation (NSVE) large-signal simulation method is employed to evaluate both static characteristics and large-signal performance parameters of these devices. This simulation approach enables precise modeling of nonlinear phenomena, such as avalanche multiplication and transit-time effects, which are critical in determining the output RF power and efficiency of IMPATT diodes under realistic biasing and signal conditions. Simulation results indicate that DDR 3C-SiC IMPATT oscillators consistently deliver superior RF output power across the 140 GHz to 1.0 THz frequency range compared to their diamond-based counterparts. This is attributed to the relatively higher carrier mobility of 3C-SiC, which reduces series resistance and enhances carrier transport. However, diamond-based IMPATT devices demonstrate better performance at lower mm-wave frequencies, particularly around 94 GHz, making diamond a suitable choice for applications targeting this frequency band. Overall, the study concludes that both 3C-SiC and type-IIb diamond offer significant improvements over conventional Si IMPATTs, particularly in terms of power output and operational frequency range. These findings establish WBG-based DDR IMPATT oscillators as strong candidates for next-generation high-frequency solid-state sources, with potential applications in advanced radar, imaging, communication systems, and spectroscopy at mm-wave and THz frequencies.