Just like I Play WoW, Hearthstone pulls your character information directly from the Armory, and displays it in a number of ways around Facebook, including, if you so choose, on your profile pages or on your wall. A few of our commenters said they liked Hearthstone's display better, but I didn't see any major differences there -- they both display your character, class, level, and server, and both will click through to pages where you can see more stats and discuss the character with others. Hearthstone will also let you change your character's image to a custom choice and enter a bio, though I Play WoW has some customization options as well. Hearthstone has an "equipment history," so even if you shard those epics you can still brag about having them. And finally,Hearthstone will let you play with the characters right on Facebook, and you can /salute or /duel the characters of your friends.
Overall, they're both worth checking out if you want to show off some of your World of Warcraft progress on Facebook. Obviously, I Play WoW is bigger, but as our commenters pointed out, Hearthstone has some excellent features as well.