Pushkin perhaps.
Friedrich Schiller, besides Goethe.
Part of the problem of comparison is that Shakespeare is the darling of literary romanticism. All the three runner-ups above score pretty high on the Romantic Scale. Others don't, obeying different aesthetic agends, but can still rival Shakespeare as realists, social dramatists, philosophers etc. (Molière, Ibsen, Calderón).
For non-Europeans try Chikmatsu Monzaemon, the "Shakespeare of Japan" (a fairly silly European way of paying a great playwright a compliment).
He's the one who in the 18th c. thematised the dilemma of the life of the samurai class as one torn between "ninjo" (human feelings) and "giri" (duty). His plays all end tragically, with people killing their loved ones and themselves in order to do their duty and preserve honour. Chikamatsu is very good at leaving it to his audience to draw the conclusions as to whether this sense of moral obligation was worth the human costs or not.
Of course he wrote it all for the consumption of his audience, which was the merchant class, who considered the samurai weird and unpleasant people, stunting themselves emotionally in order to fulfill their duty. (It was actually illegal for samurai to attend the theatre, not that they always cared. Monzaemon himself was descended from a samurai family dismissed from service, which is how he knew his subject material.)