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This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training data set. Our results show that the $\mathbb{Z}_2\times \mathbb{Z}_2$ EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.