Although neural networks are powerful function approximators, the underlying\nmodelling assumptions ultimately define the likelihood and thus the hypothesis\nclass they are parameterizing. In classification, these assumptions are minimal\nas the commonly employed softmax is capable of representing any categorical\ndistribution. In regression, however, restrictive assumptions on the type of\ncontinuous distribution to be realized are typically placed, like the dominant\nchoice of training via mean-squared error and its underlying Gaussianity\nassumption. Recently, modelling advances allow to be agnostic to the type of\ncontinuous distribution to be modelled, granting regression the flexibility of\nclassification models. While past studies stress the benefit of such flexible\nregression models in terms of performance, here we study the effect of the\nmodel choice on uncertainty estimation. We highlight that under model\nmisspecification, aleatoric uncertainty is not properly captured, and that a\nBayesian treatment of a misspecified model leads to unreliable epistemic\nuncertainty estimates. Overall, our study provides an overview on how modelling\nchoices in regression may influence uncertainty estimation and thus any\ndownstream decision making process.\n