Everything depends on what level Spectre is at. Generally the Presence is a dick and so screws Spectre over often in the power department. Spectre himself supposedly has tons of power, but needs a host to anchor him, and when the Presence actually granted him full omnipotence, Spectre couldn't handle the sensory input and was driven nearly insane. Shazam is a skyfather level being and Spectre at that time was just ripping on all the magic in the universe, and still apparently lost. Spectre is tons of fail.
By all acounts his position should put him higher than DS, but his feats are so ambiguous and his showings are all over the place it's difficult to take anything the Spectre does seriously.
He's been knocked around by Jobberseid and actually needed to take time just putting down Captain Marvel. In Kingdom Come he couldn't do anything on his own, not even judge people until his human host at the time agreed. He's like a toned down Living Tribunal without the imposing presence and power. I have personally called the Spectre DCU's cosmic whipping boy. Whenever they need an apparent super-powerful being to come around and get slapped upside the head a few times, they call in the Spectre.
That, again, still depends on the mood of the Presence. If the Presence is serious, like, completely serious about Spectre doing a job, Spectre will be pretty damn powerful and has kicked out galaxies in the process. If the Presence feels like being lazy, half-assed, or just feels like being a dick to the Spectre, Spectre's powers won't be so great and he'll get shit in his face a lot. His power levels are all over the place and inconsistent.
The Presence is DCU's TOAA, who is always the writer at the time. DC's writers in general screw around a lot which is why the comics are so inconsistent in terms of power levels. DoV Spectre should be nigh-omnipotent and 2nd (3rd) only to the Presence itself. most other times he's only pictured around Skyfather level.