The Local DOS is computed from the Green's function of the device, and as naturally spatially resolved. It is also computed for each energy separately. For these reasons, it's a quite time-consuming calculation.
The DeviceDOS is more similar to the common DOS for bulk materials. It is not naturally spatially resolved, but we can achieve that by projecting it on lattice planes (even individual atoms, if we wanted to) and it can also be projected on angular momenta, which is not possible with the LDOS. This means the resolution of the projected DDOS is that of the lattice planes, and the energy grid comes from the DOS evaluation, which can be adjusted in post-processing.
So the DDOS calculation is typically quite a bit faster than LDOS, but less precise spatially. It's also easier to make a finer energy grid with DDOS, and it can be resolved by shell contributions. But again, it's a bit more approximate.