Recent work has shown that intelligent neighbor selection during construction can significantly enhance the performance of peer-to-peer overlay networks. While its impact on performance has been recognized, few have examined the impact of neighbor selection on network resilience. In this paper, we study the impact with a generalized cost model for overlay construction that takes into consideration different types of heterogeneity, such as node capacity and network proximity. Our simulation results show that the resulting performance improvement comes at the cost of static resilience against targeted attacks and adding random redundancy can improve the resilience significantly.