We conduct in this work a comparative study between a greedy versus limited proposals for resource aggregation in the backhaul of wireless local area networks. We consider a setting with several access points, some with excess backhaul capacity (providers), and others in shortage of it (beneficiaries) and investigate two approaches for the distribution of resources between them: a greedy one wherein each beneficiary seeks to maximize the resource it could obtain from the provider and a limited one in which the operator limits the amount of acquired resources to some limit, so as to ensure fairness between beneficiaries. We model the system using a one-to-one matching game, and compare the two approaches in three scenarios: a symmetric one with equal number of providers and beneficiaries, and asymmetric ones with higher number of either providers or beneficiaries. Our results show that the greedy scheme outperforms the limited one when the number of providers is larger than that of beneficiaries, the limited one performs best in the opposite case and ensures fairness between beneficiary access points. In all cases, both approaches outperform the random allocation scheme