Battle One : Screen
Both of these screens are amazing, Samsung is using its Super AMOLED HD display which from my experience works really well in direct sunlight. Also the colors are very brilliant and have great a more vivid look to it. It has a PPI of 441. HTC is going with a Super LCD screen, this from reports looks much more natural with pictures. It will not end up looking as well i sunlight. It has a slightly higher PPI of 461. The s4 has a 5 inch screen while the HTC One has a 4.7 so you really won't notice the different in size.
Winner : TIE
Battle two : SOC
The HTC One opted for the Snapdragon 600 quad core cpu with Adreno 320 GPU. The cpu is clocked at 1.7 GHZ, the snapdragon 600 is part of Qualccom's new family of SOC's. They are about 30% faster than the s4 pro found in the Lg Optimus G which is now on sale for $50 on sprint. So it is not revolutionary, but more evolutionary. For Revolutionary check out the snapdragon 800 or the Tegra 4. The GPU can be found in the LG Optimus G and can play any game you throw at it. The Octa will be in the s4. It is around the same speed at the snapdragon 600, possibly a tid-bit slower, but it won't show through in every day usage. The main cores are a set of quad core 1.6 GHZ, then there is another set of cores that saves power. There are also four of these. The GPU is similar to that found in the Ipad 3. It is around the same speed as the Snapdragon 600. Neither of these have a GPU that is very future proof and will likely struggle to play highe-end games within a year.
Winner : s4
The Octa wins because of it's battery saving capabilities.