The energetics and dynamics of double proton transfer (DPT) is investigated theoretically for the Watson-Crick conformation of the guanine-cytosine (GC) base pair. Using semiempirical density functional theory the isolated and DNA-embedded GC pair is considered. Differences in the energetics and dynamics of DPT thus addresses the question of how relevant studies of isolated base pairs are for the understanding of processes occurring in DNA. Two-dimensional potential energy surfaces involving the transferring hydrogen atoms and the proton donors and acceptors are presented for both systems. The DPT reaction is accompanied by a contraction of the distance between the two bases with virtually identical energetic barriers being 18.8 and 18.7 kcal/mol for the isolated and DNA-embedded system, respectively. However, the transition state for DPT in the DNA-embedded GC pair is offset by 0.1 A to larger N-H separation compared to the isolated GC pair. Using activated ab initio molecular dynamics, DPT is readily observed for the isolated base pair with a minimal amount of 21.4 kcal/mol of initial average kinetic energy along the DPT normal mode vector. On a time scale of approximately 100 fs DPT has occurred and the excess energy is redistributed. For the DNA-embedded GC pair considerably more kinetic energy is required (30.0 kcal/mol) for DPT and the process is completed within one hydrogen vibration. The relevance of studies of isolated base pairs and base pair analogs in regard of reactions or properties involving DNA is discussed.