The pc thing to do would be to say "neither" because they'll both run the same OS and lose camera features & IR blaster, but I've thought about it and the more I think about it the more the Google S4 seems to be the better buy. Not because of any spec wars, only because a lot of what the One different outside of construction was Sense 5. Without it you're just left with a 4MP camera with lackluster stock camera settings and Beats, with a $600 price tag. The S4 will lose its camera features as well, but other than that all of its novelty is in the hardware. Assuming that since the One has Beats, this S4 won't be a clean stock either. If the gestures and whatnot are baked in and stock still retains the same performance then this S4 takes the cake pretty easily. Same removable storage with option to root to store on SD, same removable battery, but with a lag free OS and updates from Google and this phone is already better than the original S4. I can't really say that this One is better than the Sense One, you just lose too much. Its not like Sense 5 was bogged down anyway, it's just stupid. But it's adaptable if you work enough with it without putting up a launcher in the meantime.
I'm thinking hard about buying one of these phones but something's just telling me to save that coin to see what the XPhone looks like or wait for a Snapdragon 800 phone to hit the market. I'm not too thrilled that this phone is $50 more than the stock One and has half the memory, even with expandable storage. Then again on the other hand, for $50 more than the Google Edition One, you could buy the developer's edition, get double the memory, and flash AOSP.
Neither one really seems like all that good of a buy.