There is a pressing need to understand the factors that predict prognosis in progressive supranuclear palsy (PSP) and corticobasal syndrome (CBS), with high heterogeneity over the poor average survival. We test the hypothesis that the magnitude and distribution of connectivity changes in PSP and CBS predict the rate of progression and survival time, using datasets from the Cambridge Centre for Parkinson-plus and the UK National PSP Research Network (PROSPECT-MR). Resting-state functional MRI images were available from 146 participants with PSP, 82 participants with CBS, and 90 healthy controls. Large-scale networks were identified through independent component analyses, with correlations taken between component time series. Independent component analysis was also used to select between-network connectivity components to compare with baseline clinical severity, longitudinal rate of change in severity, and survival. Transdiagnostic survival predictors were identified using partial least squares regression for Cox models, with connectivity compared to patients' demographics, structural imaging, and clinical scores using five-fold cross-validation. In PSP and CBS, between-network connectivity components were identified that differed from controls, were associated with disease severity, and were related to survival and rate of change in clinical severity. A transdiagnostic component predicted survival beyond demographic and motion metrics but with lower accuracy than an optimal model that included the clinical and structural imaging measures. Cortical atrophy enhanced the connectivity changes that were most predictive of survival. Between-network connectivity is associated with variability in prognosis in PSP and CBS but does not improve predictive accuracy beyond clinical and structural imaging metrics.