Which antiepileptic medication has the broadest spectrum?

Depends: To be called broad-spectrum, an AED has to be tested against a broad spectrum of seizure types. The major "broad-spectrum" aeds in common use are valproic acid, lamotrigine, topiramate, levetiracetam, phenobarbital, and lacosamide. They will differ in efficacy, tolerability & side effect profile for each patient. Often, finding the right AED regimen for anyone is trial and error.

Not many: The classical broad spectrum meds include depakote, perhaps topamax, vimpat, (lacosamide) keppra. Occasionally, Lamictal may cover the variations. Whether Lyrica should be considered this way remains to be seen. The ancient drugs such as dilantin, trileptal, Phenobarbital are not in the least, broad spectrum.

No clear winner: Some are more broad spectrum than others. This category includes: valproate, levetiracetam, zonisamide, lamotrigine, and topiramate. Some of this is based on clinical experience rather than strict clinical trials. And, it does not mean that some other aeds can't cover multiple seizure types. Realize that some highly effective aeds can sometimes make some seizure types worse.