The personalities of the characters even seems different, between the two texts. I've compared the opening scene, depicting an argument between Apollo and Death, and the latter character, who is almost meek in the Web translation, eats up the stage in Hughes', blustering for whole pages about what a most basic and dreadful cosmic force he is after Apollo makes the faux pas of calling him a god. While doing so, he makes metaphoric references to morphine and nuclear bombs, and one gets the sense that he's so sure of his badassedness that he doesn't really care how shockingly anachronistic he sounds.
Looking at the cover of this book, I see it actually says "Translated and adapted by Ted Hughes". So there you go. I'm really looking forward to seeing this production, and thinking that I'll likely audition for it.
Things to do first: read this whole play, and also see the MITCP production of Happy Birthday, Wanda June this weekend.