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The imminent advent of large-scale green hydrogen (H2) production raises the central question of which of the two options, transporting "green" molecules, or transporting "green" electrons, is the most cost-effective one. This paper proposes a first-of-its-kind mathematical framework for the optimal integrated planning of electricity and H2 infrastructure for transporting large-scale variable renewable energy (VRE). In contrast to most existing works, this work incorporates essential nonlinearities such as voltage drops due to losses in high-voltage alternating current (HVAC) and high-voltage direct current (HVDC) transmission lines, losses in HVDC converter stations, reactive power flow, pressure drops in pipelines, and linepack, all of which play an important role in determining the optimal infrastructure investment decision. Capturing these nonlinearities requires casting the problem as a nonconvex mixed-integer nonlinear program (MINLP), whose complexity is further exacerbated by its large size due to the relatively high temporal resolution of RES forecasts. This work then leverages recent advancements in convex relaxations to instead solve a tractable alternative in the form of a mixed-integer quadratically constrained programming (MIQCP) problem. The impact of other fundamental factors such as transmission distance and RES capacity is also thoroughly analysed on a canonical two-node system. The integrated planning model is then demonstrated on a real-world case study involving renewable energy zones in Australia.