Mobile network operators are deploying IPv6 to their mobile networks in recent years, to support ever increasing mobile and IoT devices. They also adopt IPv4-IPv6 transition techniques to provide connectivity from their IPv6 networks to IPv4 networks. Since IPv6 deployment to mobile network is still in an early stage, the performance assessment on IPv6 based mobile network is needed, regarding both IPv6 and IPv4. In this paper, we focus on assessing the performance of IPv6 based mobile networks. We first analyze the detailed TCP connection procedures in accordance with the different IP versions that the end hosts use. Based on the analysis result, we suggest improvement points to speed up the connection establishment. We also compare the performance difference between IPv6 and IPv4 by measuring the connection establishment time to 40 popular dual-stack websites. We witnessed that IPv4 can be connected faster than IPv6 in most cases because of the immaturity of the IPv6 infrastructure.