We study Pareto efficient mechanisms in matching markets when the number of agents is large and individual preferences are randomly drawn from a class of distributions, allowing for both common and idiosyncratic shocks. We provide a broad set of circumstances under which, as the market grows large, all Pareto efficient mechanisms---including top trading cycles (with an arbitrary ownership structure), serial dictatorship (with an arbitrary serial order), and their randomized variants---produce a distribution of agent utilities that in the limit coincides with the utilitarian upper bound. This implies that Pareto efficient mechanisms are uniformly asymptotically payoff equivalent ``up to the renaming of agents.'' Hence, when the conditions of our model are met, policy makers need not discriminate among Pareto efficient mechanisms based on the aggregate payoff distribution of participants.