The gigantic growth of the internet communication technology has illustrated its value and benefits to private businesses, government organizations, worldwide professionals, academic institutes and individuals over the past few years. The size and range of computing devices connected to the internet, substantially increased because of IPv6 and offers the potential to establish a much more powerful internet compared to the IPv4. IPv6 developed by the IETF to deal with a shortage of IP addresses under IPv4. New features of IPv6 enhance packet processing speeds over routers, switches and end systems. These improved features will have different traffic characteristics than IPv4. The internet traffic which was earlier assumed as Poisson is now shown to have fractal characteristics as; heavy tailedness, self-similarity and long range dependency. Internet traffic showing above characteristics are found to have burstiness at multiple timescales. This behavior impacts network performance and degrades it substantially. It also increases complexity for network design and create difficulties to maintain desired QoS. IPv4 traffic has been well established as self-similar traffic. Nowadays, IPv6 forming a larger share of the internet traffic and it is pivotal to asses IPv6 with regards to fractal behavior. This will enable network designers to do necessary changes in the existing network to reconcile with IPv6. In this paper we compared IPv4 and IPv6 with respect to fractal behavioral characteristics. It is found that IPv6 shows higher degree of heavy tailedness, higher values of Hurst parameter values, higher fractal dimension values i.e. it is more self-similar, greater autocorrelation achieved even at larger lag and thus showing more burstiness.