  In this paper we give a criterion that characterizes equivalent weak crossed
products. By duality, we obtain a similar result for weak crossed coproducts
and, as a consequence, we find the conditions that assures the equivalence
between two weak crossed biproducts. As an application, we show that the main
results proved by Panaite, for Brzezi\'nski's crossed products, admits a
substantial reduction in the imposed conditions.
