  We present a study of binary mixtures of Bose-Einstein condensates confined
in a double-well potential within the framework of the mean field
Gross-Pitaevskii equation. We reexamine both the single component and the
binary mixture cases for such a potential, and we investigate in which
situations a simpler two-mode approach leads to an accurate description of
their dynamics. We also estimate the validity of the most usual dimensionality
reductions used to solve the Gross-Pitaevskii equations. To this end, we
compare both the semi-analytical two-mode approaches and the numerical
simulations of the 1D reductions with the full 3D numerical solutions of the
Gross-Pitaevskii equation. Our analysis provides a guide to clarify the
validity of several simplified models that describe mean field non-linear
dynamics, using an experimentally feasible binary mixture of an F=1 spinor
condensate with two of its Zeeman manifolds populated, m=+1 and m=-1.
