When Pope Gregory XIII issued the order to switch to the new calendar in 1582, Spain (a Catholic nation) complied immediately, and skipped ahead ten days in their calendar. England (a Protestant nation) ignored the papal edict. It eventually would adopt the Gregorian calendar, but not until 1752.

So the answer is that Cervantes died first. Shakespeare died ten days later.

(Or eleven, if Cervantes really died on the 22nd.)

Cervantes: “Dulcinea era un tranny. Deseé llamar su Lola.”

Shakespeare: “I just had an idea for a new tragedy… there would be snakes… on a plane…”

Cervantes died in Madrid on April 23, 1616; coincidentally William Shakespeare also died on that date, but not on the same day; Britain was still using the Julian calendar, whereas Spain had already adopted the Gregorian calendar. In honour of this coincidence UNESCO established April 23 as the International Day of the Book. It is worth mentioning that the Encyclopedia Hispanica claims the date widely quoted as Cervantes’ date of death, namely April 23, is the date on his tombstone which in accordance of the traditions at the time would be his date of burial rather than date of death. If this is true, according to Hispanica, then it means that Cervantes probably died on April 22 and was buried on April 23.