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Grain boundaries can exist as different grain boundary phases (also called complexions) with individual atomic structures. The thermodynamics of these defect phases in high-angle grain boundaries were studied mostly with atomistic and phase field computer simulations, but almost exclusively for special, symmetric boundaries. Here, we use molecular dynamics simulations combined with structure search methods, as well as scanning transmission electron microscopy experiments to take a step towards understanding more general grain boundaries. Using the example of Σ37c [111¯] tilt boundaries in Cu, we show how the grain boundary phase transition on a symmetric boundary plane is changed by the geometrically necessary defects introduced in inclined, asymmetric boundaries. We analyze the disconnections—which are dislocation-like line defects of grain boundaries—both in the simulations, as well as in experimental Cu and Al samples. A main finding is that defect energies can have a major influence on the stability of grain boundary phases, even at small inclinations. Furthermore, some defects are not able to effect large inclinations. At that point, defective asymmetric GB phases compete with grain boundaries faceting into the adjacent symmetric GB phases.