Various artificial neural networks developed by engineers are now proposed as models of parts of the brain, such as the ventral stream in the primate visual cortex. After being trained on large datasets, the network activations are compared to recordings of biological neurons. A key question is how much the ability to predict neural responses actually tells us. In particular, do these functional tests about neurons activation allow us to distinguish between different model architectures? We benchmark existing techniques to correctly identify a model by replacing the brain recordings with recordings from a known ground truth neural network, using the most common identification methods. Even in the setting where the correct model is among the candidates, we find that system identification performance is quite variable, depending significantly on factors independent of the ground truth architecture, such as scoring function and dataset. In addition, we show limitations of the current approaches in identifying higher-level architectural motifs, such as convolution and attention.