We extend previous studies on cold bosons in double well potentials using a Hubbard-like Hamiltonian to three dimensions and relax the one-level assumption. We identify the criteria to distinguish between different regimes of parameters in which different physical phenomena can be found. We characterize the eigenstates in all these regimes and show that Macroscopic Superposition (MS) states, i.e. NOON or NOON-like states, with a non-zero orbital angular momentum, are found in the interactions dominated or Fock regime. We show that, in the one dimensional case, MS states are very sensitive to small imperfections in a symmetric potential. Nevertheless, a *embedded* MS state is obtained again for certain *resonant* values of the tilt between wells. This is the key to obtain these states in the dynamical propagation of a Bose-Einstein condensate initially localized in one of the wells. We show that, for a properly prepared tilt between wells, MS states are realized periodically along the quantum sloshing of the cold bosons, thus paving the way for their experimental observation. We outline how to extend these results to the three dimensional case.