Winner-take-all (WTA) mechanisms are an important component of many cognitive models. For example, they are often used to decide between multiple choices or to selectively direct attention. Here we compare two biologically plausible, spiking neural WTA mechanisms. We first provide a novel spiking implementation of the well-known leaky, competing accumulator (LCA) model, by mapping the dynamics onto a population-level representation. We then propose a two-layer spiking independent accumulator (IA) model, and compare its performance against the LCA network on a variety of WTA benchmarks. Our findings suggest that while the LCA network can rapidly adapt to new winners, the IA network is better suited for stable decision making in the presence of noise.