The PS4 also has hUMA, the One does not. It's an AMD technology (hardware-based) that allows the CPU and GPU to use the exact same resources in memory without having to copy them. While both consoles have unified memory there still can't be any direct memory sharing (both the CPU and GPU using data at the same address). With hUMA that is possible, so there is no longer any need to copy data in-memory, which may greatly improve graphics performance.
However, it requires some work in the engine, so there is no performance difference if developers don't code for hUMA. First games won't benefit from it. But you can count on it that Naughty Dog and other PS-exclusive studios will work on it and it'll produce some impressive results.
ExtremeTech had an interesting conclusion. While for launch titles the only difference will be the base hardware differences (shader amount and memory speed) it'll be the long-term developments that will make the differences more apparent. While Microsoft bets heavily on cloud technology Sony has pulled the hardware card, with faster and more advanced components. Both will need developers to code for them, both could make a big difference.
(Personally, I have more trust in Sony's more conventional approach. Cloud offloading for real-time rendering is still something I don't think is all that interesting and is limited to a pretty small subset of all the computations needed. More hardware power however is something that everything always benefits from.)