We investigate the classical and quantum metrology of performing parameter estimation with interacting trapped bosons, which theoretically treat by a self-consistent many-body approach of the multiconfigurational Hartree type. Focusing on a tilted double-well geometry, we compare a self-consistently determined and monitored two-mode truncation, with dynamically changing orbitals, to the conventional two-mode approach of fixed orbitals, where only Fock space coefficients evolve in time. We demonstrate that, as a consequence, various metrological quantities associated to a concrete measurement such as the classical Fisher information and the maximum likelihood estimator are deeply affected by the orbitals' change during the quantum evolution. Self-consistency of the quantum many-body dynamics of interacting trapped ultracold gases thus fundamentally affects the attainable parameter estimation accuracy of a given metrological protocol.

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