GaN/AlGaN and InGaN/GaN quantum wells (QWs) are investigated as the active region for room-temperature strong exciton-photon coupling in high-quality AlInN/(Al)GaN microcavities (MCs). Angular resolved photoluminescence (PL) measurements performed on an AlInN/AlGaN MC with GaN/AlGaN QWs reveal cavity polariton dispersion curves. A vacuum-field Rabi splitting of 30 meV is observed, from which an exciton oscillator strength of 4.8x10(13) cm(-2) per QW is deduced, a value ten times larger than for InGaAs QWs. In contrast, the PL spectra of an InGaN/GaN QW MC do not exhibit such an anticrossing behavior as should be expected from the strong-coupling regime (SCR). By modeling cavity absorption and PL spectra at the resonance, the conditions, in terms of inhomogeneous excitonic broadening, for the observation of the SCR in these nitride MCs are determined.