Localization with noisy distance measurements is a critical problem in many applications of wireless sensor networks. Different localization algorithms offer different tradeoffs between accuracy and hardware resource requirements. In order to provide insight into selecting the best algorithm that optimizes this tradeoff, this paper evaluates the accuracy, memory, and computational requirements of two approaches that may be taken in localization: neural networks and Kalman filters. In this paper, we quantitatively compare the localization performance of a Multi-Layer Perceptron (MLP) neural network, PV, and PVA models of the Extended Kalman filter. Our experimental results show that the MLP neural network has weaker self-adaptivity than the Extended Kalman filters; however, the MLP can potentially achieve the highest localization accuracy and requires the least amount of computational and memory resources.