The physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential is captured by a two-component two-site Bose-Hubbard model [1]. A crucial aspect of this system is that it can host relevant entangled many-body states, e.g., Schrödinger catlike states. The richness of the binary-mixture in a double-well is the possibility of having not only spatial entanglement but also quantum correlations between the two species. Taking the atom-atom interactions within each species and among the two species as variable parameters, the many-body properties of the ground state are fully characterized by means of quantum information tools, such as the Schmidt gap or the von Neumann entropy complemented by usual many-body techniques like the computation of the condensed fractions.