The dynamic structure factor of entangled solutions of one symmetric and two asymmetric high molar mass styrene-b-ethylene-alt-propylene (SEP) and the parent styrene-b-isoprene (SI) diblock copolymers in the common solvent toluene was thoroughly studied by photon correlation spectroscopy. The incomplete hydrogenation transforms the I-block of SI into a random heteropolymer block. In turns out that this acts as enhanced composition polydispersity on both static and dynamic structure factor. In the mean-field regime of the disordered phase, the decay of the composition fluctuations in SI and SEP changes from a pure relaxational (q-independent rate) for SI to a pure diffusive (q(2)-dependent rate) character for SEP in a controlled way.