you'll have to specify which version of doctor destiny is this, his portrayal varies greatly from one arc to another.
For instance, in the beginning of gaiman's sandman series, he was able to take control of the materioptikon and use it to cause planetary (only limited to earth) havoc, and dream of the endless had to trick him to actually beat him.
in JLA classified 4th parallel arc this same materioptikon was used to create infinite universes.
In morrison's JLA he was able to project his dreaming self into the real world (without actually being aware) and warp the entire universe, and it took 7 JLA members to project themselves from the dreaming as well (which made them virtually omnipotent) to actually defeat him.
In a superman/batman arc he was able to create an illusion which he put superman and batman in, in then end, from what i recall, batman dedeuced that it was an illusion and together they eventually beat him.
so as you can see, he jumps from being a multiversal threat, to universal, to abstract, to planetary, to superman/batman level.
it was explained in the first scan, they projected their dream-selves from the dreaming, realm of dream of the endless, to the real world, hence everything they think of (or dream of) can happen.
but since they were on equal footing with destiny (who did the same thing), they couldn't just will him out of existence