The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. We find that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the $\gamma$ and $\beta$ parameters of the parameterized post-Newtonian formalism, by doing this we find relative uncertainties for the estimation of both parameters as measured by an observer at the endpoint of the array. Afterwards, we switch our strategy and consider estimating the parameters through the probability of the observable of detection in coincidence, which depends on the quantum states entering the array. Considering separable states and two-mode squeezing vacuum states yields significant improvements in the estimation of the $\gamma$ parameter, while the estimation of $\beta$ does not improve significantly. Finally, we implement Bayesian estimation for both approaches and find that the estimation of $\beta$ through measurement of time delays is not improved, while the estimation of $\gamma$ is dramatically enhanced. Also, a similar analysis shows that using coincidence detection probability outperforms all other methods and allows to make precise estimations for both parameters.