Deep learning provides new data-driven tools to relate neural activity to perception and cognition, aiding scientists in developing theories of neural computation that increasingly resemble biological systems both at the level of behavior and of neural activity. But what in a deep neural network should correspond to what in a biological system? This question is addressed implicitly in the use of comparison measures that relate specific neural or behavioral dimensions via a particular functional form. However, distinct comparison methodologies can give conflicting results in recovering even a known ground-truth model in an idealized setting, leaving open the question of what to conclude from the outcome of a systems comparison using any given methodology. Here, we develop a framework to make explicit and quantitative the effect of both hypothesis-driven aspects—such as details of the architecture of a deep neural network—as well as methodological choices in a systems comparison setting. We demonstrate via the learning dynamics of deep neural networks that, while the role of the comparison methodology is often de-emphasized relative to hypothesis-driven aspects, this choice can impact and even invert the conclusions to be drawn from a comparison between neural systems. We provide evidence that the right way to adjudicate a comparison depends on the use case—the scientific hypothesis under investigation—which could range from identifying single-neuron or circuit-level correspondences to capturing generalizability to new stimulus properties