  In this paper, we investigate the scattering properties of the hyperbolic
BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen
many-particle systems with three independent coupling constants. Utilizing the
recently established action-angle duality between these classical integrable
models, we construct their wave and scattering maps. In particular, we prove
that for both particle systems the scattering map has a factorized form.
