I've never paid the matter much attention but tend to lean, largely from inertia, toward the Stratfordians. But I've always wondered: did de Vere publish much under his own name and, if so, how does the language -- the vocabulary, sentence structure, phrasing, etc. -- line up with that of "Shakespeare." I thought there were computer programs that could compare two texts (of reasonable length) and estimate the probability that they were written by the same person.
There are. And they have been very successful in making attributions and solving literary mysteries. One of these programs demonstrated that Christopher Marlowe made some contributions to some of the "iffy" works in the Shakespeare canon that scholars have been arguing about for years but did not contribute to any of the principal, widely-accepted plays and poetry. If the supporters of de Vere are confident, they'll submit his works to this type of analysis as well.
Personally, I think the subject is fascinating, and I'd love to know who the real author of the Shakespeare plays was. I can't believe it was an uneducated, untravelled guy from a two-bit village who left not a single book, manuscript, or paper in his will. But the mystery is endlessly enchanting, isn't it?