I think that it's important to realize just what an EEG is and how it is used in a clinical setting. There are established baselines and norms for humans and animals used in experimentation, and the point is generally to identify states and abnormalities in reference to that baseline. Unlike an EKG, an EEG doesn't really tell much of a story, compared to say, fMRI or a PETscan.
The neurological activity of dogs can be compared to other dogs, but to people? Consider using an EEG on a crow: you would see a very different graph from a mammal, but would you be able to tell anything meaningful without establishing a great deal of baseline work, and tests? Of course not. EEG is a crude tool, and best used on humans and other animals for whom the requisite research has been performed.
I wonder if the core question here isn't about how actual brain functions differ between humans and other animals, in which case the EEG really gets in the way, rather than offering a source of illumination. Again, consider our friend the crow, which uses radically different structures to perform feats we usually consider to be the realm of our prefrontal cortex, and frontal lobe. Only through dissection, observation of behaviors, and modern imaging techniques has this become apparent. An EEG might show increased activity, but what does that mean out of context? Is the crow thinking of how it will retrieve a snack, is it recognizing your face, or is it just ready to take a crap?