A fundamental question for computational neuroscience is how to assess neural response similarity between a mechanistic model and the brain. We propose to map models to brains using the same set of transforms that map animal subjects to each other for the same species and brain area. We show that identifying a good transform class requires taking aspects of the mechanism underlying the brain responses into account, specifically the non-linear activation function. We therefore introduce a transform class, Inverse-Linear-Nonlinear-Poisson (ILNP), that accounts for the effect of the biological activation function. On an electro-physiological dataset of 31 mouse subjects, ILNP increases same-area similarity scores across subjects while maintaining inter-area separability compared to ridge regression and soft matching. We also find that a transform class of this kind better differentiates between various models of the mouse visual stream with respect to brain predictivity, though for some model comparisons, soft matching does better. We hypothesize that integrating some neuron-level tuning properties into the mechanistic constraints of ILNP is a promising next step in characterizing a good inter-animal transform class in order to better assess model accuracy.