Balls. I'm in a theatrical career and when I stack Shakespeare up against someone like say, Pinter, Ionesco, or Buchner, he's comparable. Not superior. I'll take Woyzeck over Hamlet any day of the week.
If we're talking in literary terms, then yeah, Shakespeare's pretty damn good. Macbeth rocks my world. King Lear and Richard III are nice too. The rest, hit and miss. Romeo and Juliet is full of cardboard characters. Winter's Tale is comedy in name only.
Greatest Playwright Ever? Maybe Bill's on the podium, but he ain't going home with the gold.