We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We find that, while the assortative correlation enhances the structural robustness against attack, the disassortative correlation significantly improves the transport efficiency of the network under consideration. This finding might shed light on the reason why some networks in the real world prefer assortative correlation and others prefer disassortative one.