By means of molecular dynamics simulations, we investigate the structural relaxation in disordered random copolymers and lamellar phases of gradient copolymers, containing chemical species of very different mobilities. Two models have been investigated: a generic bead spring system and a MARTINI coarse-grained model of a polyester resin. The lamellar phase of the gradient copolymer is formed by domains rich in one species and poor in the other one, which are separated by broad interfaces. Unlike in strongly segregated block copolymers, there is a finite probability of finding monomers of a given species at any position within the domains rich in the other species. A direct consequence of this feature is that monomers can probe very different chemical environments, and because of the strong dynamic asymmetry between the two components, their relaxation are characterized by an extreme dynamic heterogeneity. This is confirmed by an analysis of dynamic correlators as a function of the distance to the interface. In the case of random copolymers long-range ordering is not possible, and local microsegregation results in a much weaker dynamic heterogeneity. The former features are consistent with the experimental observation of narrow glass transitions in random copolymers but extremely broad ones in lamellar gradient copolymers.