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Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond-fluctuation model, where differences in the interaction energies between non-bonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a non-bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long-chain dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths $N_\mathrm{c}$ are calculated from the packing length of the chains. These are combined with a local mobility $\mu$ determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients $D_\mathrm{c}=\mu/N_\mathrm{c}$. We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients $D/D_\mathrm{c}$ as a function of reduced chain length $N/N_\mathrm{c}$. The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length twenty at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends., Comment: 12 pages, 13 figures, editorial changes