I can't speak to personal experience with any of the above phones, but I've done a fair bit of research in the new phones because I'm close between the One and the S4. Here's my quick high notes for the S4 and One:
S4 - Great screen, super fast parts, SD card, and good software if that's your thing, and good camera.
One - very good screen, almost super fast parts, great overall performance, neat software if that's your thing, and great low light camera.
iPhone - it's an iPhone. If you've used one in the past several years, it's going to be pretty much the same. When iOS 7 hits, things will get interesting...that's a maybe though.
My dark horses are the new Motorola phones. I'm currently on a Razr (2011), which I've really appreciated much more since 4.2.2 was given to me. The new features on the Moto lines are pretty sweet, but they aren't flagship hardware specs. Then again, they might be better than the sum of their parts.
I will say this is a great time to be in the market for a new phone. Tons of great options. Good luck! And for anyone who's going to be choosing soon!