When $X$ is a product system of Morita equivalence bimodules, we show that the reduced crossed product of the gauge coaction is Morita equivalent to the C$^*$-algebra $\A$. We also characterize the Cuntz-Nica-Pimsner algebras for compactly aligned product systems over quasi-lattice ordered groupoids. We show that the full cross sectional C*-algebras of Fell bundles of Morita equivalence bimodules are isomorphic to the related Cuntz-Nica-Pimsner algebras under certain conditions.