Phages, like many parasites, tend to have small genomes and may encode autonomous functions or manipulate those of their hosts'. Recombination functions are essential for phage replication and diversification. They are also nearly ubiquitous in bacteria. The E. coli genome encodes many copies of an octamer (Chi) motif that upon recognition by RecBCD favors repair of double strand breaks by homologous recombination. This might allow self from non-self discrimination because RecBCD degrades DNA lacking Chi. Bacteriophage Lambda, an E. coli parasite, lacks Chi motifs, but escapes degradation by inhibiting RecBCD and encoding its own autonomous recombination machinery. We found that only half of 275 lambdoid genomes encode recombinases, the remaining relying on the host's machinery. Unexpectedly, we found that some lambdoid phages contain extremely high numbers of Chi motifs concentrated between the phage origin of replication and the packaging site. This suggests a tight association between replication, packaging and RecBCD-mediated recombination in these phages. Indeed, phages lacking recombinases strongly over-represent Chi motifs. Conversely, phages encoding recombinases and inhibiting host recombination machinery select for the absence of Chi motifs. Host and phage recombinases use different mechanisms and the latter are more tolerant to sequence divergence. Accordingly, we show that phages encoding their own recombination machinery have more mosaic genomes resulting from recent recombination events and have more diverse gene repertoires, i.e. larger pan genomes. We discuss the costs and benefits of superseding or manipulating host recombination functions and how this decision shapes phage genome structure and evolvability.