We study the relative intensity noise (RIN) per unit bandwidth in polariton laser diodes (LDs) for two pumping geometries, namely, the direct electrical and the intracavity ones as originally described in I. Iorsh et al. [Phys. Rev. B 86, 125308 (2012)], by using rate equations including Langevin noise sources that are adapted from equations employed to describe conventional semiconductor LDs. The obtained expressions for the RIN, which can be used for all inorganic semiconductor polariton LDs, are specifically applied to the case of III-nitride devices. It is highlighted that for frequencies larger than the relaxation resonance frequency the expected minimum RIN of polariton LDs-whatever the pumping geometry-is equal to the standard quantum limit (2h nu/P-0). The general RIN line shape as a function of frequency and optical output power is discussed for the two geometries and simplified expressions for the RIN are given. Then a comprehensive account of the expected evolution of the linewidth of III-nitride polariton LDs upon increasing pumping strength is also given by considering the most advanced theories available to date. The modified Schawlow-Townes linewidth is estimated from the effective ground-state polariton lifetime at threshold, leading to a predicted linewidth as narrow as similar to 15 MHz at room temperature for the two pumping geometries when using a consistent set of parameters for III-nitride polariton LDs.