Understanding the link between the brain's anatomy and its function through computer simulations of neural tissue models is a widely used approach in computational neuroscience. This technique enables rapid prototyping and testing of hypotheses, allowing researchers to bridge the scales of biological phenomena. Until recently, the constant trend of improvement in computational power has supported an exponential growth in the scale and level of detail of in silico experiments. However, a systematic characterization of the performance landscape has not yet been carried out. In this work we intend to capture intrinsic computational properties of the existing mod- elling abstractions and answer questions about the intricate relationship between simulation algorithms and modern hardware architecture. Our first contribution is a novel set of hardware- agnostic metrics that enables us to bring focus to the heterogeneous landscape of brain tissue models. We develop a methodology able to capture subtle differences between cell-based models and quantify their impact on performance based on hardware features. We show that lumping simulation experiments together by referring to numbers of neurons and synapses without further detail hides fundamental differences in computational and hardware require- ments across models. In addition to analysing different neuron representations, we investigate the impact of biological heterogeneity on the performance of a cortical microcircuit model. Our analysis indicates that while general-purpose computers have until now sustained high- performance simulations of all brain tissue models, the next generation of in silico models will require hardware tailored to the underlying abstraction. We find that all formalisms saturate the memory bandwidth with a fairly small number of shared memory threads, but the reasons behind this are quite different: conductance-based models are dominated by the large memory traffic of clock-driven kernels, while current-based models are most affected by event-driven execution and memory latency. In distributed simulations the latency of the interconnect fabric is the root cause for a significant degradation in performance. We argue that performance analyses such as ours are required to enable the next generation of brain tissue simulations - or else scientific progress risks being hindered by the presence of severe hardware bottlenecks. Our methodology provides a common tool to facilitate the communication between modellers, developers and hardware designers in order to sustain the larger memory and performance requirements of future brain tissue simulations.