We report on the characterization and analysis of a GaN-based distributed feedback laser diode (DFB-LD) with 3rd-order laterally etched sidewall gratings centered at a wavelength of 420 nm. We also compare the device parameters with two commonly used Fabry-Perot (FP) devices operating at 450 nm and 520 nm. Intrinsic properties of the devices were extracted, including damping factor, carrier and photon lifetimes, modulation efficiency, differential gain, and parasitic capacitance. These parameters showed that the DFB exhibits a lower damping rate and parasitic capacitance while demonstrating a higher modulation efficiency, indicating that the DFB shows good potential for communications applications. Additionally, spectral linewidth of a GaN DFB is reported. To the authors' knowledge, this is the first demonstration of parameter extraction and spectral linewidth measurement for GaN-based DFB-LDs.