The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.