For external xbox one hard drives there is two main choices. 3.5" drives and 2.5" drives. 2.5" drives are almost always powered by the usb port. They turn off with the xbox one. 3.5" drives are powered by a separate power cable. So they don't turn off with the xbox one. But they usually go into a lower power mode once they cool down/console is off.
3.5" drives are larger and put out more heat (not really a lot, but if you have a confined space with not much air flow it may be a problem). But have larger capacities and are usually faster than 2.5" drives.
2.5" drives have a max capacity at the moment of 2tb. While 3.5" drives have a largest capacity of 12tb (I believe, but very costly).
For the 2 drives you listed people will say Seagate is worse than Western Digital but both drives can/could fail at any time. I would get the Seagate drive since its 1tb larger for only 7 bucks more.
USB 3 drives will be faster than the internal drive for reading from. But if you want something even faster than that there is two options to get. Either an SSD (has to be larger than 256gb). This is usually less than 100 bucks. But you also need to get an external storage case for it. With an SSD you are paying a big premium for speed. Usually a 3tb drive is around 100 bucks. While you will probably be getting an ssd and an external storage drive for around the same. So 256gb vs 3,000gb.
Or you can get a hybrid mechanical drive that has flash memory on it to improve load times. These are faster than a regular drive, but not as fast as an SSD. They are in available in larger sizes 1, 2, 4tb. They are more expensive than a normal hard drive. And you will also need an external hard drive case. Those are your options available.
And most external hard drives usually only include 1 year warranty. Because they expect people to be moving them around constantly. Bumping and banging a hard drive around is not very good for it. But most will last for a few years at the minimum.
