Structural and electronic properties of hexagonal (h-) and cubic (c-) phase AlGaInN quaternary alloys are investigated using a unified and accurate local-density approximation-1/2 approach under the density-functional theory framework. Lattice bowing parameters of h- (and c-) phase AlGaN, AlInN, InGaN, and AlGaInN alloys are extracted as 0.006 (-0.007), 0.040 (-0.015), 0.014 (-0.011), and -0.082 (0.184) Å, respectively. Bandgap bowing parameters of h- (and c-) phase AlGaN, AlInN, InGaN, and AlGaInN alloys are extracted as 1.775 (0.391), 3.678 (1.464), 1.348 (1.164), and 1.236 (2.406) eV, respectively. Direct-to-indirect bandgap crossover Al mole fractions for c-phase AlGaN and AlInN alloys are determined to be 0.700 and 0.922, respectively. Under virtual crystal approximation, electron effective masses of h- and c-phase AlGaInN alloys are extracted and those of c-phase alloys are observed to be smaller than those of the h-phase alloys. Overall, c-phase AlGaInN alloys are shown to have fundamental material advantages over the h-phase alloys such as smaller bandgaps and smaller effective masses, which motivate their applications in light emitting- and laser diodes.