The advantages of tensor- over matrix-based methods have been recently demonstrated in the context of functional magnetic resonance imaging (fMRI) blind source unmixing. However, these methods rely on the assumption of a Gaussian distribution for the noise, which suggests a least squares criterion for the tensor decomposition. One can instead argue that a Rician model for the fMRI noise is much more accurate and hence alternative cost functions should also be investigated. In this paper, β-divergences are used to parametrize the Canonical Polyadic Decomposition (CPD) fitting to fMRI data and the effect of β on the source separation performance is evaluated, for different values of signal to noise ratio (SNR). Our results confirm that the commonly used squared error is not the best choice, particularly at low SNRs.