On looks alone, the HTC One wipes the floor with the Galaxy S4. I'd argue it's the best designed Android phone ever. Deftly juggling size and weight with the use of more premium materials, the HTC One has a design that should even make Apple jealous. It's solid, but not too heavy. Thin, but not uncomfortable to hold.
The S4, on the other hand, is made of plastic and fake chrome. That said, it managed to fit a 5-inch screen and bigger battery into the same exact chassis as its predecessor. And it has a removable panel, offering access to the battery and microSD slot. That gives it some versatility the HTC One doesn't have.