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Home Care Services (HCS) delivery is a quite recent and challenging problem motivated by the ever increasing age of population and the consequent need to reduce hospitalization costs. Integer Linear Programming (ILP) models have been recently proposed in [5] to formulate a very general HCS problem, with the aim at balancing the operator workload. In fact, in Home Care setting “equity” criteria are crucial to guide the decisions. “Efficiency” criteria, i.e., the minimization of the operating costs, are essential as well. The aim of this paper is thus to compare equity criteria versus efficiency criteria in HCS. Preliminary computational results on a set of real instances are presented and analysed. Specifically, two alternative “balancing” objective functions are compared via optimization and simulation, by showing their impact on diverse relevant Quality of Service indicators, including cost indicators.