The PS4 doesn't install the full game while the Xbox downloads an update/installs the whole game to the drive.
What I don't understand is why both are still using sata II drives.
The reason why the HDD is a SATA2 one is because it doesn't fill the available bandwidth for SATA2. The only type of drives which would make full use of a SATA3 connection is SSDs, but as they are more expensive than HDDs so if MS included one it would have bumped the price of the console up a fair bit more.
That been said I only know for certain that the Xbox One has a SATA 2 HDD, I'm not too sure if the interface is SATA2 or SATA3. If its SATA3 then you could install an SSD for a boost, but that will invalidate your warranty.
You're telling me too do the right thing while climbing out a window!?!?