Restriction-modification (RM) systems are the most ubiquitous bacterial defence systems against bacteriophages. Using genome sequence data, we showed that RM systems are often shared among bacterial strains in a structured way. Examining the network of interconnections between bacterial strains within genera, we found that many strains share more RM systems than expected compared with a suitable null model. We also found that many genera have a larger than expected number of bacterial strains with unique RM systems. We used population dynamics models of closed and open phage-bacteria ecosystems to qualitatively understand the selection pressures that could lead to such network structures with enhanced overlap or uniqueness. In our models, we found that the phages impose a selection pressure that favours bacteria with greater number of RM systems, and higher overlap of RM systems with other strains, but in bacteria-dominated states, this is opposed by the increased cost-to-growth rate of these bacteria. Similar to what we observed in the genome data, we found that two distinct bacterial strategies emerge - strains either have a greater overlap than expected, or, at the other extreme, have unique RM systems. The former strategy appears to dominate when the repertoire of available RM systems is smaller but the average number of RM systems per strain is larger.