In-vivo and in-vitro experiments are routinely used in neuroscience to unravel brain functionality. Although they are a powerful experimentation tool, they are also time-consuming and, often, restrictive. Computational neuroscience attempts to solve this by using biologically-plausible and biophysically-meaningful neuron models, most prominent among which are the conductance-based models. Their computational complexity calls for accelerator-based computing to mount large-scale or real-time neuroscientific experiments. In this paper, we analyze and draw conclusions on the class of conductance models by using a representative modeling application of the inferior olive (InfOli), an important part of the olivocerebellar brain circuit. We conduct an extensive profiling session to identify the computational and data-transfer requirements of the application under various realistic use cases. The application is, then, ported onto two acceleration nodes, an Intel Xeon Phi and a Maxeler Vectis Data Flow Engine (DFE). We evaluate the performance scalability and resource requirements of the InfOli application on the two target platforms. The analysis of InfOli, which is a real-life neuroscientific application, can serve as a useful guide for porting a wide range of similar workloads on platforms like the Xeon Phi or the Maxeler DFEs. As accelerators are increasingly populating High-Performance Computing (HPC) infrastructure, the current paper provides useful insight on how to optimally use such nodes to run complex and relevant neuron modeling workloads.