We report the vibrational and collision energy dependence of cross sections and product branching in the reaction of C2H2+ with CD3OD, CD3OH, and CH3OD. We also report axial recoil velocity distributions, along with modeling. At low collision energies, reaction is mediated by a picosecond lifetime complex of the [C2H2:methanol](+) form. The bottleneck that controls overall reaction efficiency appears to be formation of the complex, and reactivity is influenced by collision energy and C2H2+ CC stretch excitation, but not by bending vibration. The most energetically favorable exit channel from the complex is isomerization to covalently bound C3H6O+ complexes, but this does not occur. Instead the [C2H2:methanol](+) decays by breakup to C2H2+CH4O+, C2H3+CH2OH+, and C2H+CH3OH2+ channels. Changes in the branching with available energy provide some insight into the nature of the transition states that control decay of the complex. As collision energy is raised above similar to 1 eV, the reaction gradually becomes direct, i.e., the collision time drops to well below the rotational period of the collision complex (< similar to 0.5 ps). In this regime, the dominant charge transfer and hydride abstraction products mostly form in large impact parameter collisions. At high energies there is little dependence of either reaction efficiency or product branching on collision energy or reactant vibrational state, suggesting that both are probably controlled largely by collision geometry.