The circadian clock modulates key physiological processes in many organisms. This widespread role of circadian rhythms is typically characterized at the molecular level by profiling the transcriptome at multiple time points. Subsequent analysis identifies transcripts with altered rhythms between control and perturbed conditions, that is, are differentially rhythmic (DiffR). Commonly, Venn diagram analysis (VDA) compares lists of rhythmic transcripts to catalog transcripts with rhythms in both conditions, or that have gained or lost rhythms. However, unavoidable errors in rhythmicity detection propagate to the final DiffR classification resulting in overestimated DiffR. We show using artificial experiments on biological data that VDA indeed produces excessive false DiffR hits both in the presence and absence of true DiffR transcripts. We review and benchmark hypothesis testing and model selection approaches that instead compare circadian amplitude and phase of transcripts between the two conditions. These methods identify transcripts that ‘gain’, ‘lose’, ‘change’, or have the ‘same’ rhythms; the third category is missed by VDA. We reanalyzed three studies on the interplay between metabolism and the clock in the mouse liver that used VDA. We found not only fewer DiffR transcripts than originally reported, but VDA overlooked many relevant DiffR transcripts. Our analyses confirmed some and contradicted other conclusions in the original studies and also generated novel insights. Our conclusions equally apply to circadian studies using other omics technologies. We believe that avoiding Venn diagrams and using our convenient r‐package comparerhythms will improve the reliability of analyses in chronobiology.