It's possible to replace the Xbox One's 500GB hard drive, but Microsoft doesn't want you to and the potential upgrades are significantly less noticeable than the PS4 replacement, Engadget reports.
Adobe techie Brian Williams replaced the Xbox One HDD with a 500GB Samsung EVO SSD and a Seagate 1TB hybrid SSHD, and found the boot time for Call of Duty: Ghosts improved incrementally: 35 seconds for the built-in HDD, 27.7 seconds for the SSHD and 27 seconds for the SSD. An SSD replacement in the PS4 improved Killzone: Shadow Fall's boot time from 60 seconds to 39 seconds.
Those who simply want more storage in their Xbox One can follow Juvenal1's Linux-based how-to or watch Williams' video walkthrough of the process. The Xbox One will eventually support USB external storage, so this particular replacement dance isn't necessary, though it certainly is complicated.