Simultaneously showing an observer two incompatible displays, one to each eye, causes binocular rivalry, during which the observer regularly switches between perceiving one eye's display and perceiving the other. Observers differ in the rate of this perceptual cycle, and these individual differences have been reported to correlate with differences in the perceptual switch rate for other bistable perception phenomena. Identifying which psychological or neural factors explain this variability can help clarify the mechanisms underlying binocular rivalry and of bistable perception generally. Motivated by the prominent theory that perceptual switches during binocular rivalry are brought about by neural adaptation, we investigated whether perceptual switch rates are correlated with the strength of neural adaptation, indexed by visual aftereffects. We found no compelling evidence for such correlations. Moreover, we did not corroborate previous findings that switch rates are correlated between binocular rivalry and other forms of bistable perception. This latter nonreplication prompted us to perform a meta-analysis of existing research into correlations among forms of bistable perception, which revealed that evidence for such correlations is much weaker than is generally believed. By showing no common factor linking individual differences in binocular rivalry and in our other paradigms, these results fit well with other work that has shown such common factors to be rare among visual phenomena generally.