Coexistence between great tits Parus major and blue tits Cyanistes caeruleus, but also other hole‐nesting taxa, constitutes a classic example of species co‐occurrence resulting in potential interference and exploitation competition for food and for breeding and roosting sites. However, the spatial and temporal variations in coexistence and its consequences for competition remain poorly understood. We used an extensive database on reproduction in nest boxes by great and blue tits based on 87 study plots across Europe and Northern Africa during 1957–2012 for a total of 19,075 great tit and 16,729 blue tit clutches to assess correlative evidence for a relationship between laying date and clutch size, respectively, and density consistent with effects of intraspecific and interspecific competition. In an initial set of analyses, we statistically controlled for a suite of site‐specific variables. We found evidence for an effect of intraspecific competition on blue tit laying date (later laying at higher density) and clutch size (smaller clutch size at higher density), but no evidence of significant effects of intraspecific competition in great tits, nor effects of interspecific competition for either species. To further control for site‐specific variation caused by a range of potentially confounding variables, we compared means and variances in laying date and clutch size of great and blue tits among three categories of difference in density between the two species. We exploited the fact that means and variances are generally positively correlated. If interspecific competition occurs, we predicted a reduction in mean and an increase in variance in clutch size in great tit and blue tit when density of heterospecifics is higher than the density of conspecifics, and for intraspecific competition, this reduction would occur when density of conspecifics is higher than the density of heterospecifics. Such comparisons of temporal patterns of means and variances revealed evidence, for both species, consistent with intraspecific competition and to a smaller extent with interspecific competition. These findings suggest that competition associated with reproductive behaviour between blue and great tits is widespread, but also varies across large spatial and temporal scales.