Implanted neural recording system vs Electroencephalography
EEG records a rough average of activity from a large area of the brain, because it is located far away from the actual neurons. There is no way to separate out the activity of individual or even small groups of cells; instead, you record lower frequency synchronous activity among whole populations.

Implanted systems can record from small groups or sometimes even single neurons, which greatly increases the amount of information available.

Depending on the purposes of the recording or research, EEG might be sufficient; in other cases, implantable electrodes are required. EEG is sufficient to monitor sleep/wake cycles, for example; there is no need to record intracranially to monitor sleep (unless perhaps you are studying mechanisms of sleep itself). Implanted electrodes are often used before surgery to remove parts of the brain that are causing seizures. Using ECoG (basically an "EEG on the dura" rather than on the skull) or depth electrodes allows the surgeon to know more precisely which area is causing seizures, hopefully leading to a more successful surgery and needing to resect less tissue.

Implanted electrodes are also commonly used in animal experiments to learn about how single neurons and small populations encode or process information.