Transitioning an infrastructure the size of the Internet is no small feat. We are in the midst of such a transition, \ie from IPv4 to IPv6. IPv6 was standardized 15~years ago, but until recently there were few incentives to adopt it. The allocation of the last large block of IPv4 addresses changed that, and migrating to an IPv6 Internet has become more urgent. This migration is, however, still rife with uncertainties and challenges. The goal of this paper is to provide insight into this transition, and possibly make it smoother. The focus is on the ``network,'' and the paper reports on extensive measurements that compare and contrast IPv6 and IPv4. Two important hypotheses, denoted as H1 and H2, were identified and validated. H1 argues that the IPv6 and IPv4 data planes now perform by and large comparably. In contrast, H2 points to routing differences as the primary culprit behind occurrences of poorer IPv6 performance. In other words, promoting IPv6 and IPv4 peering parity is probably the single most effective step towards equal IPv6 and IPv4 performance