Energy efficiency is of principal concern when designing sensor networks for distributed measurement applications. Wireless sensor networks comprising many energy-efficient nodes with asynchronous sleep/awake cycles offer a low power, cost effective and simple alternative to planned and synchronized networks. Detecting the presence of a target is a common problem in many sensor network applications. We develop a mathematical model to represent an asynchronous sensor network and provide a comparison of this type of a network against a benchmark scheduled network for a detection application. This comparison is drawn first assuming that the probability of detection is one if the target is present within a sensing radius of a sensor node. A more realistic comparison of the networks is then made by relaxing this assumption. We show that for applications where a moderate detection coverage is sufficient, the asynchronous sensor network compares well with a scheduled network and is thus a promising alternative to traditional sensor network architectures.