In terms of speed i would say both are almost equal it is really depending on your own preference. If you need option of adding storage and a removal battery and also a whole lot of s/w features S4 is a good choice for you. If all of those are not important to you and you are more concern on how the phone feels when held i would say HTC One hands down lol. As in terms of s/w to my opinion HO is more elegant and does it job. However its really up to your preference.

I was from those Samseng clan (oops.. Samsung). I disposed S4 for this awesome One.
No looking back after that and definitely no regrets.
Never I became so excited getting and using a new phone b4 the One.
Used most makes and models b4 but the One is really amazing phone with features I really2 like and serve my needs.
Cannot agree more to all advices above.
It's u who will be using not ur friend.
Get the unit which can fulfill ur needs tho I personally believe that the One is the best there is currently.