“The History Boys” received six Tonys, more than any other production, also taking home prizes for actor, Richard Griffiths; director, Nicholas Hytner; featured actress, Frances de la Tour; and two design prizes, sets and lighting. While “Jersey Boys,” picked up the top musical prize and received four Tonys, its main competitor, “The Drowsy Chaperone,” the Canadian-born musical that affectionately celebrates Broadway’s past, won more awards — five — including best book and score.”