Partially inspired by features of computation in visual cortex, deep neural networks compute hierarchical representations of their inputs. While these networks have been highly successful in machine learning, it is still unclear to what extent they can aid our understanding of cortical function. Several groups have developed metrics that provide a quantitative comparison between representations computed by networks and representations measured in cortex. At the same time, neuroscience is well into an unprecedented phase of large-scale data collection, as evidenced by projects such as the Allen Brain Observatory. Despite the magnitude of these efforts, in a given experiment only a fraction of units are recorded, limiting the information available about the cortical representation. Moreover, only a finite number of stimuli can be shown to an animal over the course of a realistic experiment. These limitations raise the question of how and whether metrics that compare representations of deep networks are meaningful on these data sets. Here, we empirically quantify the capabilities and limitations of these metrics due to limited image and neuron sample spaces. We find that the comparison procedure is robust to different choices of stimuli set and the level of sub-sampling that one might expect in a large scale brain survey with thousands of neurons. Using these results, we compare the representations measured in the Allen Brain Observatory in response to natural image presentations. We show that the visual cortical areas are relatively high order representations (in that they map to deeper layers of convolutional neural networks). Furthermore, we see evidence of a broad, more parallel organization rather than a sequential hierarchy, with the primary area VISp (V1) being lower order relative to the other areas.