As mentioned above, it's all up to your needs. For me personally, the HTC One is a better choice because I prefer LCDs over Super Amoled displays and the plastic shell of the S4 simply can't match the aluminium unibody of the HTC One. I don't mind the non-expandable storage and unremovable battery, but you might want to take these things into consideration. Software-wise, Sense 5 appeals more to me. TouchWiz seems a bit old-fashioned. Regarding performance, the difference is negligible. Numbers aside, in real world usage you won't feel a dramatic difference in performance between the two handsets.
Long story short, I would suggest the HTC One, but that's because I like it better. Yes, my reply is biased towards the One, but then again, everyone has different priorities. It's all up to you in the end. Make the choice based on your preferences, because you won't make a terrible choice either way. Good luck!