On a technical level, the slightly smaller 4.7-inch screen of the HTC One gives it a higher pixel density than the 4.99-inch Galaxy S4: 469 pixels per inch vs 441 pixels per inch.
That means the HTC One is technically sharper. In the real world, however, it would take an obsessive person to notice the difference in clarity.
But the HTC One display is not only brighter than the Galaxy S4, it has a more accurate color profile too. That means photos and videos appear closer to the way your eye would have seen it in real life.