If you are prone to dropping your phone or otherwise concerned about the screen cracking get a decent case. One thing to keep in mind is that the One despite it's truly awesome build materials was recently rated as one of the most unfixable phones currently available whereas the S4 ranks very high in fixibility.
so if I get the One and ever have issues with it, I gotta make sure to get insurance and hope to get a replacement/refurb for a decent price. I was looking at getting the One from newegg (it's $129.99 with upgrade from them, OR $149 with upgrade from amazon, vs $199.99 from sprint. S4 is $199 from both), and I think I can get sprint's insurance on it even if I don't purchase from them, though I don't think they'd handle the repair or replacement like they would if I did purchase from them, so it may be worth the extra $70 down the line. or pay $199 for the S4 from sprint for a plastic phone that can at least be more easily fixed if anything were to happen.
Wanna know why?
It's P.L.A.S.T.I.C. !
My 3 and a half year olds dump truck bought at dollar general feels more elegant....and sturdy. I bet though, you break the One, you walk out with a new one if you have insurance. With the S4, they will try to fix it and gouge the crap out of the plastic like they did on my hTc Evo. Actually, they broke the plastic housing in 4 places....I got a brand new one in the box....
I'm coming from a plastic phone, and I've learned to cover it up in screen protectors, skins (decal girl has nice ones, though it's probably not as necessary with these phones that are all screen, now, but my old phone body was sensitive to chipping in the front and corners), and cases, so in the end, the aluminum isn't going to be showing or felt much. and I do like being able to pull out my battery when my phone is frozen and won't turn off with the power button. I would hope that when they get geriatric neither phone has problems with freezing and ignoring power off buttons, but in two years, who knows?