The winner-take-all (WTA) computation in networks of recurrently connected neurons is an important decision element of many models of cortical processing. However, analytical studies of the WTA performance in recurrent networks have generally addressed rate-based models. Very few have addressed networks of spiking neurons, which are relevant for understanding the biological networks themselves, and also for the development of neuromorphic electronic neurons that commmunicate by action-potential like address-events. Here, we make steps in that direction by using a simplified Markov model of the spiking network to examine analytically the ability of a spike-based WTA network to discriminate the statistics of inputs ranging from stationary regular to non-stationary Poisson events. Our work extends previous theoretical results showing that a WTA recurrent network receiving regular spike inputs can select the correct winner within one interspike interval. We show firstly for the case of spike rate inputs, that input discrimination and the effects of self-excitation and inhibition on this discrimination are consistent with results obtained from the standard rate-based WTA models. We also extend this discrimination analysis of spiking WTAs to non-stationary inputs with time-varying spike rates resembling statistics of real-world sensory stimuli. We conclude that spiking WTAs are consistent with their continuous counterparts for steady-state inputs, but they also exhibit high discrimination performance with non-stationary inputs.