We introduce \textsc{CAT}, a framework designed to evaluate and visualize the \emph{interplay} of \emph{accuracy} and \emph{response consistency} of Large Language Models (LLMs) under controllable input variations, using multiple-choice (MC) benchmarks as a case study. Current evaluation practices primarily focus on model capabilities such as accuracy or benchmark scores and, more recently, measuring consistency is being considered an essential property for deploying LLMs in high-stake, real-world applications. We argue in this paper that although both dimensions should still be evaluated independently, their inter-dependency also need to be considered for a more nuanced evaluation of LLMs. At the core of \textsc{CAT} are the \emph{Consistency-Accuracy Relation (CAR)} curves, which visualize how model accuracy varies with increasing consistency requirements, as defined by the \emph{Minimum-Consistency Accuracy (MCA)} metric. We further propose the \emph{Consistency-Oriented Robustness Estimate (CORE)} index, a global metric that combines the area and shape of the CAR curve to quantify the trade-off between accuracy and consistency. We present a practical demonstration of our framework across a diverse set of generalist and domain-specific LLMs, evaluated on multiple MC benchmarks. We also outline how \textsc{CAT} can be extended beyond MC tasks to support long-form, open-ended evaluations through adaptable scoring functions.