Bacterial persistence represents a simple of phenotypic heterogeneity, whereby a proportion of cells in an isogenic bacterial population can survive exposure to lethal stresses such as antibiotics. In contrast, genetically based antibiotic resistance allows for continued growth in the presence of antibiotics. It is unclear, however, whether resistance and persistence are complementary or alternative evolutionary adaptations to antibiotics. Here, we investigate the co‐evolution of resistance and persistence across the genus Pseudomonas using comparative methods that correct for phylogenetic nonindependence. We find that strains of Pseudomonas vary extensively in both their intrinsic resistance to antibiotics (ciprofloxacin and rifampicin) and persistence following exposure to these antibiotics. Crucially, we find that persistence correlates positively to antibiotic resistance across strains. However, we find that different genes control resistance and persistence implying that they are independent traits. Specifically, we find that the number of type II toxin–antitoxin systems (TAs) in the genome of a strain is correlated to persistence, but not resistance. Our study shows that persistence and antibiotic resistance are complementary, but independent, evolutionary adaptations to stress and it highlights the key role played by TAs in the evolution of persistence.